bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Applications of Artamonov-Quillen-Suslin Theorems to Metabelian Inner Rank and Primitivity
Authors: Gupta C. K. , Gupta N. D. , Noskov G. A.
Published: December 2010

For any variety of groups, the relative inner rank of a given groupG is defined to be the maximal rank of the -free homomorphic images of G. In this paper we explore metabelian inner ranks of certain one-relator groups. Using the well-known Quillen-Suslin Theorem, in conjunction with an elegant result of Artamonov, we prove that if r is any "Δ-modular" element of the free metabelian group Mn of rank n > 2 then the metabelian inner rank of the quotient group Mn/(r) is at most [n/2]. As a corollary we deduce that the metabelian inner rank of the (orientable) surface group of genus k is precisely k. This extends the corresponding result of Zieschang about the absolute inner ranks of these surface groups. In continuation of some further applications of the Quillen-Suslin Theorem we give necessary and sufficient conditions for a system g = (g1,..., gk) of k elements of a free metabelian group Mn, k ≤ n, to be a part of a basis of Mn. This extends results of Bachmuth and Timoshenko who considered the cases k = n and k < n — 3 respectively.
Additive Automorphic Functions and Bloch Functions
Authors: Aulaskari Rauno , Lappan Peter
Published: December 2010

A function f analytic in the unit disk D is said to be strongly uniformly continuous hyperbolically, or SUCH, on a set E ⊂ D if for each ∊ > 0 there exists a δ > 0 such that |f(z) — f(z')| < ∊ whenever z and z' are points in E and the hyperbolic distance between z and z' is less than δ. We show that f is a Bloch function in D if and only if |f| is SUCH in D. A function f is said to be additive automorphic in D relative to a Fuchsian group F if, for each γ ∊ Γ, there exists a constant Aγ such that f(γ(z)) =f(z) + Aγ. We show that if an analytic function f is additive automorphic in D relative to a Fuchsian group Γ, where Γ is either finitely generated or if the fundamental region F of Γ has the right kind of structure, and if |f| is SUCH in F, then f is a Bloch function. We show by example that some restrictions on Γ are needed.
Singularities and Higher Torsion in Symplectic Cobordism
Authors: Botvinnik Boris I. , Kochman Stanley O.
Published: December 2010

In this paper we construct higher two-torsion elements of all orders in the symplectic cobordism ring. We begin by constructing higher torsion elements in the symplectic cobordism ring with singularities using a geometric approach to the Adams- Novikov spectral sequence in terms of cobordism with singularities. Then we show how these elements determine particular elements of higher torsion in the symplectic cobordism ring.
A Normal Form in Free Fields
Authors: Cohn Paul M. , Reutenauer Christophe
Published: December 2010

We give a normal form for the elements in the free field, following the lines of the minimization theory of noncommutative rational series.
Isometric Shift Operators on C(X)
Authors: Farid F. O. , Varadarajan K.
Published: December 2010

Recently A. Gutek, D. Hart, J. Jamison and M. Rajagopalan have obtained many significiant results concerning shift operators on Banach spaces. Using a result of Holsztynski they classify isometric shift operators on C(X) for any compact Hausdorff space X into two (not necessarily disjoint) classes. If there exists an isometric shift operator T: C(X) → C(X) of type II, they show that X is necessarily separable. In case T is of type I, they exhibit a paticular infinite countable set of isolated points in X. Under the additional assumption that the linear functional Γ carrying f ∊ C(X) to Tf(p) ∊ is identically zero, they show that D is dense in X. They raise the question whether D will still be dense in X even when Γ ≠ 0. In this paper we give a negative answer to this question. In fact, given any integer l ≥ 1, we construct an example of an isometric shift operator T: C(X) —> C(X) of type I with X \ having exactly / elements, where is the closure of D in X.
Isometric Characterizations of ℓnp Spaces
Authors: Komorowski Ryszard
Published: December 2010

The paper establishes some characterizations of spaces in terms of p-summing or p-nuclear norms of the identity operator on the given space E.

In particular, for an n-dimensional Banach space E and I ≤ p < 2, E is isometric to if and only if πp(E*) ≥ n1/p and E* has cotype p' with the constant one.

Furthermore, spaces are characterized by inequalities for p-summing norms of operators related to the John's ellipsoid of maximal volume contained in the unit ball of E.
Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities
Authors: Lakey Joseph D.
Published: December 2010

Wiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates
Littlewood-Paley and Multiplier Theorems for Vilenkin-Fourier Series
Authors: Young Wo-Sang
Published: December 2010

Let S2jf be the 2j-th partial sum of the Vilenkin-Fourier series of f ∊ L1, and set S2-1f = 0. For , we show that the ratio

is contained between two bounds (independent of f) . From this we obtain the Marcinkiewicz multiplier theorem for Vilenkin-Fourier series.
Products of Decomposable Positive
Operators
Authors: Quinn Terrance
Published: December 2010

In recent years there has been a growing interest in problems of factorization for bounded linear operators. We first show that many of these problems properly belong to the category of C*-algebras. With this interpretation, it becomes evident that the problem is fundamental both to the structure of operator algebras and the elements therein. In this paper we consider the direct integral algebra with separable and infinite dimensional. We generalize a theorem of Wu (1988) and characterize those decomposable operators which are products of non-negative decomposable operators. We do this by first showing that various results on operator ranges may be generalized to “measurable fields of operator ranges”.
Finite Clones Containing All Permutations
Authors: Haddad L. , Rosenberg I. G.
Published: December 2010

Let A be a finite set with |A| > 2. We describe all clones on A containing the set SA of all permutations of A among its unary operations. (A clone on A is a composition closed set of finitary operations on A containing all projections). With a few exceptions such a clone C is either essentially unary or cellular i.e. there exists a monoid M of self-maps of A containing SA such that either C = (= all essentially unary operations agreeing with some f ∊ M) or C = ∪ Гh where 1 < h ≤ |A| and Гh consists of all finitary operations on A taking at most h values. The exceptions are subclones of Burle's clone or of its variant (provided |A| is even).
Weakly Projective and Weakly Injective Modules
Authors: Jain S. K. , López-Permouth S. R. , Oshiro K. , Saleh M. A.
Published: December 2010

A module M is said to be weakly N-projective if it has a projective cover π: P(M) ↠M and for each homomorphism : P(M) → N there exists an epimorphism σ:P(M) ↠M such that (kerσ) = 0, equivalently there exists a homomorphism :M ↠N such that σ= . A module M is said to be weakly projective if it is weakly N-projective for all finitely generated modules N. Weakly N-injective and weakly injective modules are defined dually. In this paper we study rings over which every weakly injective right R-module is weakly projective. We also study those rings over which every weakly projective right module is weakly injective. Among other results, we show that for a ring R the following conditions are equivalent:

(1) R is a left perfect and every weakly projective right R-module is weakly injective.

(2) R is a direct sum of matrix rings over local QF-rings.

(3) R is a QF-ring such that for any indecomposable projective right module eR and for any right ideal I, soc(eR/eI) = (eR/eJ)n for some positive integer n.

(4) R is right artinian ring and every weakly injective right R-module is weakly
projective.

(5) Every weakly projective right R-module is weakly injective and every weakly injective right R-module is weakly projective.
Unification in Varieties of Groups: Nilpotent Varieties
Authors: Albert Michael H. , Lawrence John
Published: December 2010

In this paper we show that any system of equations over a free nilpotent
group of class c is either unitary or miliary. In fact,
such a system either has a most general solution (akin to the most general
solution of a system of linear dipohantine equations), or every solution has a
proper generalization. In principle we provide an algorithm for determining
whether or not a most general solution exists, and exhibiting it if it
does.
Exponential Boundedness and Amenability of Open Subsemigroups of Locally
Compact Groups
Authors: Jaworski Wojciech
Published: December 2010

Let G be a connected amenable locally compact
group with left Haar measure λ. In an earlier work Jenkins claimed that
exponential boundedness of G is equivalent to each of
the following conditions: (a) every open subsemigroup S
⊆ G is amenable; (b) given and a compact
K ⊆ G with nonempty
interior there exists an integer n such that (c) given a signed
measure of compact support
and nonnegative nonzero f ∈ L
∞(G), the condition
v * f ≥ 0 implies
v(G) ≥ 0. However,
Jenkins‚ proof of this equivalence is not complete. We give a complete proof. The
crucial part of the argument relies on the following two results: (1) an open
σ-compact subsemigroup S ⊆ G
is amenable if and only if there exists an absolutely continuous probability
measure μ on S such that lim
for every
s ∈ S; (2) G is
exponentially bounded if and only if for every nonempty
open subset U ⊆ G.
A Lower Bound for the Real Genus of a Finite Group
Authors: May Coy L.
Published: December 2010

Let G be a finite group. The real
genus ρ(G) is the minimum algebraic
genus of any compact bordered Klein surface on which G
acts. Here we obtain a good general lower bound for the real genus of the group
G. We use the standard representation of
G as a quotient of a non-euclidean crystallographic
group by a bordered surface group. The lower bound is used to determine the real
genus of several infinite families of groups; the lower bound is attained for some
of these families. Among the groups considered are the dicyclic groups and some
abelian groups. We also obtain a formula for the real genus of the direct product
of an elementary abelian 2-group and an “even” dicyclic group. In addition, we
calculate the real genus of an abstract family of groups that includes some
interesting 3-groups. Finally, we determine the real genus of the direct product
of an elementary abelian 2-group and a dihedral group.
Zeros of Iterated Integrals of Polynomials
Authors: Borwein Peter B. , Chen Weiyu , Dilcher Karl
Published: December 2010

The operator Im is defined as m-fold indefinite integration with zero constants of integration. The zero distribution of Im(p) for polynomials p is studied in general, and for two special classes of polynomials in detail. The main results are: (i) The zeros of In(Pn), where Pn(𝑧) is the n-th Legendre polynomial, converge to a certain algebraic curve; (ii) the zeros of an integer) converge to pieces of a circle and of two "Szegö curves".
Units in Integral Group Rings for Order pq
Authors: Hoechsmann Klaus
Published: December 2010

For any finite abelian group A, let Ω(A) denote the group of units in the integral group ring which are mapped to cyclotomic units by every character of A. It always contains a subgroup Y(A), of finite index, for which a basis can be systematically exhibited. For A of order pq, where p and q are odd primes, we derive estimates for the index [Ω(A) : Y(A)]. In particular, we obtain conditions for its triviality.
Quasi-Regular Dirichlet Forms: Examples and Counterexamples
Authors: Röckner Michael , Schmuland Byron
Published: December 2010

We prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loop spaces, and certain Fleming- Viot processes.
Homology of Abelian Coverings of Links and Spatial Graphs
Authors: Sakuma Makoto
Published: December 2010

We give (1) a formula of the first Betti numbers of abelian coverings of links in terms of the Alexander ideals, (2) certain estimates of the orders of the torsion parts of their first homology groups in terms of the Alexander polynomials, and (3) a structure theorem of the first homology groups of -coverings of spatial graphs. As an application, we generalize a result of E. Hironaka on polynomial periodicity of the first Betti numbers in certain towers of abelian coverings of complex surfaces.
Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)
Authors: Asmar Nakhlé , Berkson Earl , Gillespie T. A.
Published: December 2010

In the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.
Twisted Group Rings Whose Units Form an FC-Group
Authors: Bovdi Victor
Published: December 2010

Let U(KλG) be the group of units of the infinite twisted group algebra KλG over a field K. We describe the FC-centre ΔU of U(KλG) and give a characterization of the groups G and fields K for which U(KλG) = ΔU. In the case of group algebras we obtain the Cliff-Sehgal-Zassenhaus theorem.
A Boundary Rigidity Problem For Holomorphic Mappings on Some Weakly Pseudoconvex Domains
Authors: Huang Xiaojun
Published: December 2010

In this paper, we study the boundary version of the classical Cartan theorem. We show that for some weakly pseudoconvex domains, when a holomorphic self-mapping has a sufficiently high order of contact (which depends only on the geometric properties of the domains) with the identical map at some boundary point, then it must coincide with the identity.
Comparison Theorems of Liapunov-Razumikhin Type for NFDEs With Infinite Delay
Authors: Haddock John R. , Ruan Shigui , Wu Jianhong , Xia Huaxing
Published: December 2010

Some comparison theorems of Liapunov-Razumikhin type are provided for uniform (asymptotic) stability and uniform (ultimate) boundedness of solutions to neutral functional differential equations with infinite delay with respect to a given phase space pair. Examples are given to illustrate how the comparison theorems and stability and boundedness of solutions depend on the choice(s) of phase space(s) and are related to asymptotic behavior of solutions to some difference and integral equations.
Local Character Expansions for Supercuspidal Representations of U(3)
Authors: Murnaghan Fiona
Published: December 2010

The topic of this paper is the relationship between characters of irreducible supercuspidal representations of the p-adic unramified 3 x 3 unitary group and Fourier transforms of invariant measures on elliptic adjoint orbits in the Lie algebra. We prove that most supercuspidal representations have the property that, on some neighbourhood of zero, the character composed with the exponential map coincides with the formal degree of the representation times the Fourier transform of a measure on one elliptic orbit. For the remainder, a linear combination of the Fourier transforms of measures on two elliptic orbits must be taken. As a consequence of these relations between characters and Fourier transforms, the coefficients in the local character expansions are expressed in terms of values of Shalika germs. By calculating which of the values of the Shalika germs associated to regular nilpotent orbits are nonzero, we determine which irreducible supercuspidal representations have Whittaker models. Finally, the coefficients in the local character expansions of three families of supercuspidal representations are computed.
Weak-Star Continuous Analytic Functions
Authors: Aron R. M. , Cole B. J. , Gamelin T. W.
Published: December 2010

Let 𝒳 be a complex Banach space, with open unit ball B. We consider the algebra of analytic functions on B that are weakly continuous and that are uniformly continuous with respect to the norm. We show these are precisely the analytic functions on B that extend to be weak-star continuous on the closed unit ball of 𝒳**. If 𝒳* has the approximation property, then any such function is approximable uniformly on B by finite polynomials in elements of 𝒳*. On the other hand, there exist Banach spaces for which these finite-type polynomials fail to approximate. We consider also the approximation of entire functions by finite-type polynomials. Assuming 𝒳* has the approximation property, we show that entire functions are approximable uniformly on bounded sets if and only if the spectrum of the algebra of entire functions coincides (as a point set) with 𝒳**.
A Simple Algorithm for Deciding Primes in K[[x,y]]
Authors: Char kuo Tzee
Published: December 2010

The well-known Tschirnhausen transformation, , eliminates the second term of the polynomial xn + axn-l + …. By a mere repeated application of this transformation, one can decide whether a given element of k[[x,y]] is prime (irreducible) or not. Here K is an algebraically closed field of characteristic 0. A generalised version of Hensel's Lemma is developed for the proofs. The entire paper can be understood by undergraduate students.
Ergodic Averages for Weight Functions Moved by Non-Linear Transformations on ℝn
Authors: McIntosh David I.
Published: December 2010

Let ℝ+ denote the non-negative half of the real line, and let λ denote Lebesgue measure on the Borel sets of ℝn. A function φ: ℝn → ℝ+ is called a weight function if ʃℝn φ dλ = 1. Let (X, ℱ, μ) be a non-atomic, finite measure space, let ƒ: X → ℝ+, and suppose { Tν}ν∊ℝn is an ergodic, aperiodic ℝn-flow on X. We consider the weighted ergodic averages where is a sequence of weight functions. Sufficient as well as necessary and sufficient conditions for the pointwise, almost-everywhere convergence of are developed for a particular class of weight functions φk. Specifically, let {τk: ℝn → ℝn} be a sequence of measurable, non-singular maps with measurable, non-singular inverses such that the Radon-Nikodym derivatives dλ oτk /dλ and dλ oτk-1 / dλ are L∞ (ℝn), and such that τk and τ-1 map bounded sets to bounded sets. We examine convergence for the sequence where θk is an a.e.-convergent sequence of weight functions which are dominated by a fixed L1(ℝn) function with bounded support.
Some Values for the Rogers-Ramanujan Continued Fraction
Authors: Bernd Bruce C. , Chan Heng Huat
Published: December 2010

In his first and lost notebooks, Ramanujan recorded several values for the Rogers-Ramanujan continued fraction. Some of these results have been proved by K. G. Ramanathan, using mostly ideas with which Ramanujan was unfamiliar. In this paper, eight of Ramanujan's values are established; four are proved for the first time, while the remaining four had been previously proved by Ramanathan by entirely different methods. Our proofs employ some of Ramanujan's beautiful eta-function identities, which have not been heretofore used for evaluating continued fractions.
Residue Integrals and their Mellin Transforms
Authors: Passare Mikael , Tsikh August
Published: December 2010

Given an almost arbitrary holomorphic map we study the structure of the associated residue integral and its Mellin transform, and the relation between these two objects. More precisely, we relate the limit behaviour of the residue integral to the polar structure of the Mellin transform. We consider also ideals connected to nonisolated singularities.
є-Families of Operators in Triebel-Lizorkin and Tent Spaces
Authors: Welland Grant , Zhao Shiying
Published: December 2010

In this paper, we study the boundedness of є-families of operators on Triebel-Lizorkin with wide range of parameters. We also prove that є -families of operators are bounded from Triebel-Lizorkin spaces into (generalized) tent spaces, and obtain a characterization of certain Triebel-Lizorkin spaces in terms of tent spaces. In particular, the boundedness of fractional operators in Triebel-Lizorkin, and a sharp version of T\theorem for generalized Calderón-Zygmund operators on Triebel-Lizorkin spaces can be considered as applications of (proofs of) these results.
Carleson Measures on Spaces of Hardy-Sobolev Type
Authors: Cascante Carme , Ortega Joaquín M.
Published: December 2010

We study positive measures on 𝔹n satisfying that . for any ƒ ∈ where is the Hardy-Sobolev space in the unit ball. We obtain several computable sufficient conditions as well as some necessary conditions and establish their sharpness. We study the same problem for Besov-Sobolev spaces and give some applications to multipliers.
Decomposition of Witt Rings and Galois Groups
Authors: Mináč Ján , Smith Tara L.
Published: December 2010

To each fieldFof characteristic not 2, one can associate a certain Galois group 𝒢F, the so-calledW-group ofF, which carries essentially the same information as the Witt ringW(F)ofF. In this paper we show that direct products of Witt rings correspond to free products of these Galois groups (in the appropriate category), group ring construction of Witt rings corresponds to semidirect products ofW-groups, and the basic part ofW(F)is related to the center of 𝒢F. In an appendix we provide a complete list of Witt rings and corresponding w-groups for fieldsFwith |Ḟ/Ḟ2| ≤ 16.
A Family of Generalized Riesz Products
Authors: Dooley A. H. , Eigen S. J.
Published: December 2010

Generalized Riesz products similar to the type which arise as the spectral measure for a rank-one transformation are studied. A condition for the mutual singularity of two such measures is given. As an application, a probability space of transformations is presented in which almost all transformations are singular with respect to Lebesgue measure.
Spectra for Infinite Tensor Product Type Actions of Compact Groups
Authors: Gootman Elliot C. , Lazar Aldo J.
Published: December 2010

We present explicit calculations of the Arveson spectrum, the strong Arveson spectrum, the Connes spectrum, and the strong Connes spectrum, for an infinite tensor product type action of a compact group. Using these calculations and earlier results (of the authors and C. Peligrad) relating the various spectra to the ideal structure of the crossed product algebra, we prove that the topology of G influences the ideal structure of the crossed product algebra, in the following sense: if G contains a nontrivial connected group as a direct summand, then the crossed product algebra may be prime, but it is never simple; while if G is discrete, the crossed product algebra is simple if and only if it is prime. These results extend to compact groups analogous results of Bratteli for abelian groups. In addition, we exhibit a class of examples illustrating that for compact groups, unlike the case for abelian groups, the Connes spectrum and strong Connes spectrum need not be stable.
A Subnormal Operator and its Dual
Authors: Olin Robert F. , Yang Liming
Published: December 2010

It is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.
Central Quotients and Coverings of Steinberg Unitary Lie Algebras
Authors: Allison Bruce N. , Gao Yun
Published: December 2010

In this paper, we calculate the center and the universal covering algebra of the Steinberg unitary Lie algebra stun, where is a unital nonassociative algebra with involution and n ≥ 3.
The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism
Authors: Arlettaz Dominique
Published: December 2010

This paper shows that for the Moore spectrum MG associated with any abelian group G, and for any positive integer n, the order of the Postnikov k-invariant kn+1(MG) is equal to the exponent of the homotopy group πnMG. In the case of the sphere spectrum S, this implies that the exponents of the homotopy groups of S provide a universal estimate for the exponent of the kernel of the stable Hurewicz homomorphism hn: πnX → En(X) for the homology theory E*(—) corresponding to any connective ring spectrum E such that π0E is torsion-free and for any bounded below spectrum X. Moreover, an upper bound for the exponent of the cokernel of the generalized Hurewicz homomorphism hn: En(X) → Hn(X; π0E), induced by the 0-th Postnikov section of E, is obtained for any connective spectrum E. An application of these results enables us to approximate in a universal way both kernel and cokernel of the unstable Hurewicz homomorphism between the algebraic K-theory of any ring and the ordinary integral homology of its linear group.
A Schilder Type Theorem for Super-Brownian Motion
Authors: Fleischmann Klaus , Gärtner Jürgen , Kaj Ingemar
Published: December 2010

LetXbe ad-dimensional continuous super-Brownian motion with branching rate ε, which might be described symbolically by the "stochastic equation"a space-time white noise. A Schilder type theorem is established concerning large deviation probabilities ofXon path space asε→ 0, with a representation of the rate functional via anL2-functional on a generalized "Cameron-Martin space" of measure-valued paths.
Complemented Copies of ℓ1 and Pełczyński's Property (V*) in Bochner Function Spaces
Authors: Randrianantoanina Narcisse
Published: December 2010

Let X be a Banach space and (fn)n be a bounded sequence in L1(X). We prove a complemented version of the celebrated Talagrand's dichotomy, i.e., we show that if (en)n denotes the unit vector basis of c0, there exists a sequence gn ∈ conv(fn, fn+1,...) such that for almost every ω, either the sequence (gn(ω) ⊗ en) is weakly Cauchy in or it is equivalent to the unit vector basis of ℓ1. We then get a criterion for a bounded sequence to contain a subsequence equivalent to a complemented copy of ℓ1 in L1(X). As an application, we show that for a Banach space X, the space L1(X) has Pełczyńiski's property (V*) if and only if X does.
The Local Product Structure of Expansive Automorphisms of Solenoids and Their Associated C*-Algebras
Authors: Brenken Berndt
Published: December 2010

An explicit description of a hyperbolic canonical coordinate system for an expansive automorphism of a compact connected abelian group is given. These dynamical systems are factors of subshifts of finite type. Some properties of the associated crossed product C*-algebra are discussed. In these examples, the C* -algebras of Ruelle are crossed product algebras.
Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights II
Authors: Damelin S. B. , Lubinsky D. S.
Published: December 2010

We complete our investigations of mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdős weights W2 = e-2Q. The archetypal example is Wk,α = exp(—Qk,α), where

α > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < 4 and α ∊ ℝ Let Ln[f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn(W2, x) = pn(e-2Q, x). Then for

to hold for every continuous function ƒ:ℝ. —> ℝ satisfying

it is necessary and sufficient that α > 1/p. This is, essentially, an extension of the Erdös-Turan theorem on L2 convergence. In an earlier paper, we analyzed convergence for all p > 1, showing the necessity and sufficiency of using the weighting factor 1 + Q for all p > 4. Our proofs of convergence are based on converse quadrature sum estimates, that are established using methods of H. König.
Oscillation Criteria for Second Order Neutral Differential Equations
Authors: Li Horng-Jaan , Liu Wei-Ling
Published: December 2010

Some oscillation criteria are given for the second order neutral delay differential equation

where τ and σ are nonnegative constants,. These results generalize and improve some known results about both neutral and delay differential equations.
K-Theoretic Classification for Inductive Limit Z2 Actions on af Algebras
Authors: Elliott George A. , Su Hongbing
Published: December 2010

In this paper a K-theoretic classification is given of the C*-dynamical systems where An is finite-dimensional. Corresponding to the trivial action is the K-theoretic classification for AF algebras obtained in [3] (also see [1]).
On Degenerations of Modules With Nondirecting Indecomposable Summands
Authors: Skowroński A. , Zwara G.
Published: December 2010

Let A be a finite dimensional associative K-algebra with an identity over an algebraically closed field K, d a natural number, and modA(d) the affine variety of d-dimensional A-modules. The general linear group Gld(K) acts on modA(d) by conjugation, and the orbits correspond to the isomorphism classes of d-dimensional modules. For M and N in modA(d), N is called a degeneration of M, if TV belongs to the closure of the orbit of M. This defines a partial order ≤deg on modA(d). There has been a work [1], [10], [11], [21] connecting ≤deg with other partial orders ≤ext and ≤deg on modA(d) defined in terms of extensions and homomorphisms. In particular, it is known that these partial orders coincide in the case A is representation-finite and its Auslander-Reiten quiver is directed. We study degenerations of modules from the additive categories given by connected components of the Auslander-Reiten quiver of A having oriented cycles. We show that the partial orders ≤ext, ≤deg and < coincide on modules from the additive categories of quasi-tubes [24], and describe minimal degenerations of such modules. Moreover, we show that M ≤degN does not imply M ≤ext N for some indecomposable modules M and N lying in coils in the sense of [4].
Numerical Criteria for Very Ampleness of Divisors on Projective Bundles Over an Elliptic Curve
Authors: Alzati Alberto , Bertolini Marina , Besana Gian Mario
Published: December 2010

Let D be a divisor on a projectivized bundle over an elliptic curve. Numerical conditions for the very ampleness of D are proved. In some cases a complete numerical characterization is found.
A Constructive Brauer-Witt Theorem for Certain Solvable Groups
Authors: Herman Allen
Published: December 2010

Division algebras occurring in simple components of group algebras of finite groups over algebraic number fields are studied. First, well-known restrictions are presented for the structure of a group that arises once no further Clifford Theory reductions are possible. For groups with these properties, a character-theoretic condition is given that forces thep-part of the division algebra part of this simple component to be generated by a predeterminedp-quasi-elementary subgroup of the group, for any prime integerp. This is effectively a constructive Brauer-Witt Theorem for groups satisfying this condition. It is then shown that it is possible to constructively compute the Schur index of a simple component of the group algebra of a finite nilpotent-by-abelian group using the above reduction and an algorithm for computing Schur indices of simple algebras generated by finite metabelian groups.
Disciplined Spaces and Centralizer Clone Segments
Authors: Trnková V. , Sichler J.
Published: December 2010

Our main result implies that for any choice 1 ≤m ≤ n ≤ pof integers there exist finitary algebrasA1andA2that generate the same variety, and such that the initialk-segments of their centralizer clones coincide exactly whenk ≤ m,are isomorphic exactly whenk ≤ nand are elementarily equivalent exactly whenk ≤ p.The proof uses the existence and properties of disciplined topological spaces which we introduce and investigate here.
Constrained Approximation in Sobolev Spaces
Authors: Hu Y. K. , Kopotun K. A. , Yu X. M.
Published: December 2010

Positive, copositive, onesided and intertwining (co-onesided) polynomial and spline approximations of functions are considered. Both uniform and pointwise estimates, which are exact in some sense, are obtained.
Estimates for the Heat Kernel on SL(n,R)/ SO(n)
Authors: Sawyer P.
Published: December 2010

In [1], Jean-Philippe Anker conjectures an upper bound for the heat kernel of a symmetric space of noncompact type. We show in this paper that his prediction is verified for the space of positive definite n × n real matrices.
Limit Transitions for BC Type Multivariable Orthogonal Polynomials
Authors: Stokman Jasper V. , Koornwinder Tom H.
Published: December 2010

Limit transitions will be derived between the five parameter family of Askey-Wilson polynomials, the four parameter family of big q-Jacobi polynomials and the three parameter family of little q-Jacobi polynomials in n variables associated with root system BC. These limit transitions generalize the known hierarchy structure between these families in the one variable case. Furthermore it will be proved that these three families are q-analogues of the three parameter family of BC type Jacobi polynomials in n variables. The limit transitions will be derived by taking limits of q-difference operators which have these polynomials as eigenfunctions.
Some Adjunction-Theoretic Properties of Codimension Two Non-Singular Subvarities of Quadrics
Authors: De Cataldo Mark Andrea A.
Published: December 2010

We make precise the structure of the first two reduction morphisms associated with codimension two non-singular subvarieties of non-singular quadrics Qn, n ≥ 5. We give a coarse classification of the same class of subvarieties when they are assumed not to be of log-general-type.
Density Questions for the Truncated Matrix Moment Problem
Authors: Duran Antonio J. , Lopez-Rodriguez Pedro
Published: December 2010

For a truncated matrix moment problem, we describe in detail the set of positive definite matrices of measures μ in V2n (this is the set of solutions of the problem of degree 2n) for which the polynomials up to degree n are dense in the corresponding space L2(μ). These matrices of measures are exactly the extremal measures of the set Vn.
Twisted Hasse-Weil L-Functions and the Rank of Mordell-Weil Groups
Authors: Howe Lawrence
Published: December 2010

Following a method outlined by Greenberg, root number computations give a conjectural lower bound for the ranks of certain Mordell–Weil groups of elliptic curves. More specifically, for PQn a PGL2(Z/pnZ)–extension of Q and E an elliptic curve over Q, define the motive E ⊗ ρ, where ρ is any irreducible representation of Gal(PQn /Q). Under some restrictions, the root number in the conjectural functional equation for the L-function of E ⊗ ρ is easily computable, and a ‘–1’ implies, by the Birch and Swinnerton–Dyer conjecture, that ρ is found in E(PQn) ⊗ C. Summing the dimensions of such ρ gives a conjectural lower bound of

p2n–p2n–1–p–1

for the rank of E(PQn).
Homomorphisms From C(X) Into C*-Algebras
Authors: Lin Huaxin
Published: December 2010

Let A be a simple C*-algebra with real rank zero, stable rank one and weakly unperforated K0(A) of countable rank. We show that a monomorphism Φ: C(S2) → A can be approximated pointwise by homomorphisms from C(S2) into A with finite dimensional range if and only if certain index vanishes. In particular,we show that every homomorphism ϕ from C(S2) into a UHF-algebra can be approximated pointwise by homomorphisms from C(S2) into the UHF-algebra with finite dimensional range.As an application, we show that if A is a simple C*-algebra of real rank zero and is an inductive limit of matrices over C(S2) then A is an AF-algebra. Similar results for tori are also obtained. Classification of Hom (C(X), A) for lower dimensional spaces is also studied.
A Characterization of two Weight Norm Inequalities for One-Sided Operators of Fractional Type
Authors: Lorente Maria
Published: December 2010

In this paper we give a characterization of the pairs of weights (ω, v) such that T maps Lp(v) into Lq(ω),where T is a general one-sided operator that includes as a particular case theWeyl fractional integral. As an applicationwe solve the following problem: given a weight v, when is there a nontrivial weight ω such that T maps Lp(v) into Lq(ω)?
Isoperimetric Inequalities on Surfaces of Constant Curvature
Authors: Ku Hsu-Tung , Ku Mei-Chin , Zhang Xin-Min
Published: December 2010

In this paper we introduce the concepts of hyperbolic and elliptic areas and prove uncountably many new geometric isoperimetric inequalities on the surfaces of constant curvature.
Asymptotic Shape of Finite Packings
Authors: Böröczky KáRoly , Schnell Uwe
Published: December 2010

Let Kbe a convex body in Ed and denote by Cn the set of centroids of n non-overlapping translates of K. Forϱ > 0, assume that the parallel body conv Cn+ϱ K of convCn has minimal volume. The notion of parametric density (see [21]) provides a bridge between finite and infinite packings (see [4] or [14]). It is known that there exists a maximal ϱs(K) ≥ 1/(32d2) such that convCn is a segment for ϱ < ϱs(see [5]). We prove the existence of a minimal ϱc(K) ≤ d+ 1 such that if ϱ > ϱc and n is large then the shape of conv Cn can not be too far from the shape of K. For d= 2, we verify that ϱs= ϱc. For d≥ 3, we present the first example of a convex body with known ϱs and ϱc; namely, we have ϱs= ϱ c= 1 for the parallelotope.
Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel
Authors: Ding Yong , Lu Shanzhen
Published: December 2010

Given function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.
Murnaghan-Nakayama Rules for Characters of Iwahori-Hecke Algebras of the Complex Reflection Groups G(r, p, n)
Authors: Halverson Tom , Ram Arun
Published: December 2010

Iwahori-Hecke algebras for the infinite series of complex reflection groups G(r, p, n) were constructed recently in the work of Ariki and Koike [AK], Broué andMalle [BM], and Ariki [Ari]. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper [HR] in whichwe derivedMurnaghan-Nakayama rules for the characters of the Iwahori-Hecke algebras of the classical Weyl groups. In both papers we have been motivated by C. Greene [Gre], who gave a new derivation of the Murnaghan-Nakayama formula for irreducible symmetric group characters by summing diagonal matrix entries in Young's seminormal representations. We use the analogous representations of the Iwahori-Hecke algebra of G(r, p, n) given by Ariki and Koike [AK] and Ariki [Ari].
Intertwining Operator and h-Harmonics Associated With Reflection Groups
Authors: Xu Yuan
Published: December 2010

We study the intertwining operator and h-harmonics in Dunkl's theory on h–harmonics associated with reflection groups. Based on a biorthogonality between the ordinary harmonics and the action of the intertwining operator V on the harmonics, the main result provides a method to compute the action of the intertwining operator V on polynomials and to construct an orthonormal basis for the space of h-harmonics.
Equivariant Polynomial Automorphisms Of Θ-Representations
Authors: Kurth Alexandre
Published: December 2010

We show that every equivariant polynomial automorphism of a Θ- representation and of the reduction of an irreducible Θ-representation is a multiple of the identity.
Asymptotic Transformations of q-Series
Authors: McIntosh Richard J.
Published: December 2010

For the q–series we construct a companion q–series such that the asymptotic expansions of their logarithms as q → 1– differ only in the dominant few terms. The asymptotic expansion of their quotient then has a simple closed form; this gives rise to a new q–hypergeometric identity. We give an asymptotic expansion of a general class of q–series containing some of Ramanujan's mock theta functions and Selberg's identities.
Qp Spaces on Riemann Surfaces
Authors: Aulaskari Rauno , He Yuzan , Ristioja Juha , Zhao Ruhan
Published: December 2010

We study the function spaces Qp(R) defined on a Riemann surface R, which were earlier introduced in the unit disk of the complex plane. The nesting property Qp(R) ⊆Qq(R) for 0 < p < q < ∞ is shown in case of arbitrary hyperbolic Riemann surfaces. Further, it is proved that the classical Dirichlet space AD(R) ⊆ Qp(R) for any p, 0 < p < ∞, thus sharpening T. Metzger's well-known result AD(R) ⊆ BMOA(R). Also the first author's result AD(R) ⊆ VMOA(R) for a regular Riemann surface R is sharpened by showing that, in fact, AD(R) ⊆ Qp,0(R) for all p, 0 < p < ∞. The relationships between Qp(R) and various generalizations of the Bloch space on R are considered. Finally we show that Qp(R) is a Banach space for 0 < p < ∞.
Morse Index of Approximating Periodic Solutions for the Billiard Problem. Application to Existence Results
Authors: Bolle Philippe
Published: December 2010

This paper deals with periodic solutions for the billiard problem in a bounded open set of ℝN which are limits of regular solutions of Lagrangian systems with a potential well. We give a precise link between the Morse index of approximate solutions (regarded as critical points of Lagrangian functionals) and the properties of the bounce trajectory to which they converge.
Mittag-Leffler Theorems on Riemann Surfaces and Riemannian Manifolds
Authors: Gauthier Paul M.
Published: December 2010

Cauchy and Poisson integrals over unbounded sets are employed to proveMittag-Leffler type theorems with massive singularities as well as approximation theorems for holomorphic and harmonic functions.
The Homology of Singular Polygon Spaces
Authors: Kamiyama Yasuhiko
Published: December 2010

Let Mn be the variety of spatial polygons P = (a1, a2, … ,an) whose sides are vectors ai ∈ R3 of length |ai| = 1 (1 ≤ i ≤ n), up to motion in R3. It is known that for odd n, Mn is a smooth manifold, while for even n, Mn has cone-like singular points. For odd n, the rational homology of Mn was determined by Kirwan and Klyachko [6], [9]. The purpose of this paper is to determine the rational homology of Mn for even n. For even n, let be the manifold obtained from Mn by the resolution of the singularities. Then we also determine the integral homology of .
The Eichler Trace of ℤp Actions on Riemann Surfaces
Authors: Sjerve Denis , Yang Qing Jie
Published: December 2010

We study ℤp actions on compact connected Riemann surfaces via their associated Eichler traces.We determine the set of possible Eichler traces and determine the relationship between 2 actions if they have the same trace.
Indecomposable Almost Free Modules—The Local Case
Authors: Göbel Rüdiger , Shelah Saharon
Published: December 2010

Let R be a countable, principal ideal domain which is not a field and A be a countable R-algebra which is free as an R-module. Then we will construct an ℵ1-free R-module G of rank ℵ1 with endomorphism algebra EndRG = A. Clearly the result does not hold for fields. Recall that an R-module is ℵ1-free if all its countable submodules are free, a condition closely related to Pontryagin’s theorem. This result has many consequences, depending on the algebra A in use. For instance, if we choose A = R, then clearly G is an indecomposable ‘almost free’module. The existence of such modules was unknown for rings with only finitelymany primes like R = ℤ(p), the integers localized at some prime p. The result complements a classical realization theorem of Corner’s showing that any such algebra is an endomorphism algebra of some torsionfree, reduced R-module G of countable rank. Its proof is based on new combinatorialalgebraic techniques related with what we call rigid tree-elements coming from a module generated over a forest of trees.
Upper Bounds on |L(1, χ)| and Applications
Authors: Louboutin Stéphane
Published: December 2010

We give upper bounds on the modulus of the values at s = 1 of Artin L-functions of abelian extensions unramified at all the infinite places.We also explain how we can compute better upper bounds and explain how useful such computed bounds are when dealing with class number problems for CM-fields. For example, we will reduce the determination of all the non-abelian normal CM-fields of degree 24 with Galois group SL2(F3) (the special linear group over the finite field with three elements) which have class number one to the computation of the class numbers of 23 such CM-fields.
Smooth Formal Embeddings and the Residue Complex
Authors: Yekutieli Amnon
Published: December 2010

Let π:X → S be a finite type morphism of noetherian schemes. A smooth formal embedding of X (over S) is a bijective closed immersion X ⊂ 𝖃 , where 𝖃 is a noetherian formal scheme, formally smooth over S. An example of such an embedding is the formal completion 𝖃 = Y/X where X ⊂ Y is an algebraic embedding. Smooth formal embeddings can be used to calculate algebraic De Rham(co)homology.

Our main application is an explicit construction of the Grothendieck residue complex when S is a regular scheme. By definition the residue complex is the Cousin complex of π!OS, as in [RD]. We start with I-C. Huang's theory of pseudofunctors on modules with 0-dimensional support, which provides a graded sheaf .We then use smooth formal embeddings to obtain the coboundary operator . We exhibit a canonical isomorphism between the complex (K·x/s, δ ) and the residue complex of [RD]. When π is equidimensional of dimension n and generically smooth we show that H-nK·x/s is canonically isomorphic to to the sheaf of regular differentials of Kunz-Waldi [KW].

Another issue we discuss is Grothendieck Duality on a noetherian formal scheme 1d583 . Our results on duality are used in the construction of K·x/s.
On a Conjecture of Goresky, Kottwitz and MacPherson
Authors: Allday C. , Puppe V.
Published: December 2010

We settle a conjecture of Goresky, Kottwitz and MacPherson related to Koszul duality, i.e., to the correspondence between differential graded modules over the exterior algebra and those over the symmetric algebra.
Partial Characters and Signed Quotient Hypergroups
Authors: Rösler Margit , Voit Michael
Published: December 2010

IfGis a closed subgroup of a commutative hypergroupK, then the coset spaceK/Gcarries a quotient hypergroup structure. In this paper, we study related convolution structures onK/Gcoming fromdeformations of the quotient hypergroup structure by certain functions onKwhich we call partial characters with respect toG. They are usually not probability-preserving, but lead to so-called signed hypergroups onK/G. A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair (U(n, 1),U(n)) are discussed.
Meromorphic functions with prescribed asymptotic behaviour, zeros and poles and applications in complex approximation
Authors: Sauer A.
Published: December 2010

We construct meromorphic functions with asymptotic power series expansion in z−1 at ∞ on an Arakelyan set A having prescribed zeros and poles outside A. We use our results to prove approximation theorems where the approximating function fulfills interpolation restrictions outside the set of approximation.