bluuebunny/crossref_metadata_2025_split huggingface dataset:
Units in Integral Group Rings for Order pq
Authors: Hoechsmann Klaus 
Published: December 2010

AbstractFor 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

AbstractWe 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

AbstractWe 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

AbstractIn 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

AbstractLet 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

AbstractIn 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

AbstractSome 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

AbstractThe 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

AbstractLet 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

AbstractThe 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

AbstractLet 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

AbstractIn 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

AbstractGiven 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

AbstractIn 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

AbstractWe 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

AbstractTo 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

AbstractGeneralized 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

AbstractWe 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

AbstractIt 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.
The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism
Authors: Arlettaz Dominique 
Published: December 2010

AbstractThis 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

AbstractLetXbe 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

AbstractLet 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

AbstractAn 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

AbstractWe 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), whereα > 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 forto hold for every continuous function ƒ:ℝ. —> ℝ satisfyingit 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.
On Degenerations of Modules With Nondirecting Indecomposable Summands
Authors: Skowroński A. , Zwara G. 
Published: December 2010

AbstractLet 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

AbstractLet 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

AbstractDivision 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

AbstractOur 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.
Limit Transitions for BC Type Multivariable Orthogonal Polynomials
Authors: Stokman Jasper V. , Koornwinder Tom H. 
Published: December 2010

AbstractLimit 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

AbstractWe 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

AbstractFor 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

AbstractFollowing 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 ofp2n–p2n–1–p–1for the rank of E(PQn).
Homomorphisms From C(X) Into C*-Algebras
Authors: Lin Huaxin 
Published: December 2010

AbstractLet 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.