bluuebunny/crossref_metadata_2025 huggingface dataset:
Dedekind Completeness and the Algebraic Complexity of o-Minimal Structures
Authors: Mekler Alan , Rubin Matatyahu , Steinhorn Charles
Published: December 2010

An ordered structure is o-minimal if every definable subset is the union of finitely many points and open intervals. A theory is o-minimal if all its models are ominimal. All theories considered will be o-minimal. A theory is said to be n-ary if every formula is equivalent to a Boolean combination of formulas in n free variables. (A 2-ary theory is called binary.) We prove that if a theory is not binary then it is not rc-ary for any n. We also characterize the binary theories which have a Dedekind complete model and those whose underlying set order is dense. In [5], it is shown that if T is a binary theory, is a Dedekind complete model of T, and I is an interval in , then for all cardinals K there is a Dedekind complete elementary extension of , so that . In contrast, we show that if T is not binary and is a Dedekind complete model of T, then there is an interval I in so that if is a Dedekind complete elementary extension of .
On the Decomposition of a Representation of SOn When Restricted to SOn-1
Authors: Gross Benedict H. , Prasad Dipendra
Published: December 2010

Let k be a local field, with char(k) ≠ 2. A quadratic space V over k is a finite dimensional vector space together with a non-degenerate quadratic form Q: V → k.The special orthogonal group SO(V) consists of all linear maps T: V → V which satisfy:

Q(Tv) = Q(v) for all ν and det T = 1.
Positive Finite Energy Solutions of Critical Semilinear Elliptic Problems
Authors: Noussair Ezzat S. , Swanson Charles A. , Jianfu Yang
Published: December 2010

Existence theorems and asymptotic properties will be obtained for boundary value problems of the form in an unbounded domain Ω⊆ RN(N ≥3) with smooth boundary, where Δ denotes the TV-dimensional Laplacian, τ — (N+ 2)/ (N — 2) is the critical Sobolev exponent, and is the completion of in the L2(Ω) norm of .
Quartic Algebras
Authors: Farsi Carla , Watling Neil
Published: December 2010

In this paper we study the fixed point algebra of the automorphism of the rotation algebra , θ = p/q with p, q coprime positive integers, given by u → v-1, v → u. We give a general characterization of the fixed point algebra, determine its K-theory and consider the related crossed-product algebra ⋊Ƭ Z4.
Relative Kloosterman Integrals for GL(3): II
Authors: Jacquet Hervé
Published: December 2010

Let G′ be a quasi–split reductive group over a local field F, ƒ′ the characteristic function of a maximal compact subgroup K′ of G′, N′ a maximal unipotent subgroup of G′. We consider the orbits of maximal dimension for the action of N′ × N′ on G′ and the weighted orbital integral of f′ on such an orbit, the weight being a generic character. The resulting integral, we call a Kloosterman integral. A relative version of this construction is to consider a symmetric space S associated to a quasi-split group G, a maximal unipotent subgroup N of G, a maximal compact K of G and the orbits of maximal dimension for the action of N on S. The weighted orbital integral of the characteristic function f of K ∩ S on such an orbit is what we call a relative Kloosterman integral; the weight is an appropriate character of N. We conjecture that a relative Kloosterman integral is actually a Kloosterman integral for an appropriate group G′. We prove the conjecture in a simple case: E is an unramified quadratic extension of F,G is GL(3, E), S is the set of 3 × 3 matrices s such that the group G′ is then the quasi-split unitary group in three variables.
The Pierce-Birkhoff Conjecture for Curves
Authors: Marshall Murray
Published: December 2010

The results obtained extend Madden’s result for Dedekind domains to more general types of 1-dimensional Noetherian rings. In particular, these results apply to piecewise polynomial functions t:C → R where R is a real closed field and C ⊆ Rn is a closed 1-dimensional semi-algebraic set, and also to the associated “relative” case where t, C are defined over some subfield K ⊆ R.
Homogeneous Polynomials, Centralizers and Derivations in Rings
Authors: Divincenzo Onofrio Mario , Sagona Rosa
Published: December 2010

Letdbe a non-zero derivation on a primitive ringRandƒ(x1,…,xn) a homogeneous polynomial of degreem. We prove that the conditiond(ƒ(r1,…,rn)t) = 0, for allr1,…,rn∈R, withtdepending onr1,…,rn, forcesRto be a finite dimensional central simple algebra andƒpower-central valued onR. We also obtain bounds on [R:Z(R)] in terms ofm.
Randomization Moduli of Continuity for ℓ2-Norm Squared Ornstein-Uhlenbeck Processes
Authors: Csorgő M. , Lin Z.-Y. , Shao Q.-M.
Published: December 2010

We establish exact randomized moduli of continuity for ℓ2-norm squared independent Ornstein–Uhlenbeck processes.
On the Divisibility of Homogeneous Directed Graphs
Authors: El-Zahar M. , Sauer N. W.
Published: December 2010

Let be a finite set of finite tournaments. We will give a necessary and sufficient condition for the -free homogeneous directed graph to be divisible. That is, that there is a partition of into two classes such that neither of them contains an isomorphic copy of .
Projective and Multigraded Representations of Monomial and Multisigned Groups I. Graded Representations of a Twisted Product
Authors: Hoffman Peter
Published: December 2010

Motivated by the problem of giving a functorial (or at least uniform) description of the projective representations for wreath productsGʅSnin terms of those for G, we study a certain binary operationon the class of “cyclic covering groups with parities”. Along with setting up the basic machinery associated to representations graded by (Ζ/2)ℓ, the main result is a description of the irreducibles forin terms of a (tensorlike) product of those forAand forB.Finally we describe a programme for producing a PSH-algebra theory in this context, analogous to that of Zelevinsky for the case ℓ=0, and that of the author with with Michael Bean (structure) and with John Humphreys (applications) for the case ℓ=1
Linear Transformations on Symmetric Spaces II
Authors: Lim Ming–Huat
Published: December 2010

Let U be a finite dimensional vector space over an infinite field F. Let U(r) denote the r–th symmetric product space over U. Let T: U(r) → U(s) be a linear transformation which sends nonzero decomposable elements to nonzero decomposable elements. Let dim U ≥ s + 1. Then we obtain the structure of T for the following cases: (I) F is algebraically closed, (II) F is the real field, and (III) T is injective.
Conditional Sequence Entropy and Mild Mixing Extensions
Authors: Zhang Qing
Published: December 2010

For a measure preserving system (X, ℬ, μ, T) with a factor (Y, C, v, T) and an infinite sequence {tn}, one can define conditional sequence entropy. We present two theorems which characterize rigid and mildly mixing extensions by conditional sequence entropy. Properties of IP-systems are used to prove our main theorems.
Spectral Integration of Marcinkiewicz Multipliers
Authors: Asmar Nakhlé , Berkson Earl , Gillespie T. A.
Published: December 2010

Let X be a closed subspace of LP(μ), where μ is an arbitrary measure and 1 < p < ∞. By extending the scope of spectral integration, we show that every invertible power-bounded linear mapping of X into X has a functional calculus implemented by the algebra of complex-valued functions on the unit circle satisfying the hypotheses of the Strong Marcinkiewicz Multiplier Theorem. This result expands the framework of the Strong Marcinkiewicz Multiplier Theorem to the setting of abstract measure spaces.
On the Ideal of Veronesean Surfaces
Authors: Gimigliano A. , Lorenzini A.
Published: December 2010

We consider the blowing up of ℙ2 at s sufficiently general distinct points and its projective embedding by the linear system of the curves of a given degree through the points. We study the ideal of the resulting (Veronesean) surface and find that it can be described by two matrices of linear forms, in the sense that it is generated by the entries of the product matrix and the minors of complementary orders of the two matrices.

By cutting the surface twice with general hyperplanes, we also obtain some information about the generation (or even the resolution) of certain classes of points in projective space.
A Calculus of EPI-Derivatives Applicable to Optimization
Authors: Poliquin R. A. , Rockafellar R. T.
Published: December 2010

When an optimization problem is represented by its essential objective function, which incorporates constraints through infinite penalties, first- and secondorder conditions for optimality can be stated in terms of the first- and second-order epi-derivatives of that function. Such derivatives also are the key to the formulation of subproblems determining the response of a problem's solution when the data values on which the problem depends are perturbed. It is vital for such reasons to have available a calculus of epi-derivatives. This paper builds on a central case already understood, where the essential objective function is the composite of a convex function and a smooth mapping with certain qualifications, in order to develop differentiation rules covering operations such as addition of functions and a more general form of composition. Classes of "amenable" functions are introduced to mark out territory in which this sharper form of nonsmooth analysis can be carried out.
Covering Games and the Banach-Mazur Game: K-tactics
Authors: Bartoszynski Tomek , Just Winfried , Scheepers Marion
Published: December 2010

Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the σ-completion of J, and player TWO tries to cover the union of this sequence by playing one set at a time from J. We describe various conditions under which player TWO has a winning strategy that uses only information about the most recent k moves of ONE, and apply some of these results to the Banach-Mazurgame.
On Convex Functions Having Points of Gateaux Differentiability Which are Not Points of Fréchet Differentiability
Authors: Borwein J. M. , Fabian M.
Published: December 2010

We study the relationships between Gateaux, Fréchet and weak Hadamard differentiability of convex functions and of equivalent norms. As a consequence we provide related characterizations of infinite dimensional Banach spaces and of Banach spaces containing ł1. Explicit examples are given. Some renormings of WCG Asplund spaces are made in this vein.
Dense Subgroups of the Automorphism Groups of Free Algebras
Authors: Bryant Roger M. , Drensky Vesselin
Published: December 2010

Let F be the free metabelian Lie algebra of finite rank m over a field K of characteristic 0. The automorphism group Aut F is considered with respect to a topology called the formal power series topology and it is shown that the group of tame automorphisms (automorphisms induced from the free Lie algebra of rank m) is dense in Aut F for m ≥ 4 but not dense for m = 2 and m = 3. At a more general level, we study the formal power series topology on the semigroup of all endomorphisms of an arbitrary (associative or non-associative) relatively free algebra of finite rank m and investigate certain associated modules of the general linear group GLm(AT).
A+∞ Condition
Authors: Martín-Reyes F. J. , Pick L. , De La Torre A.
Published: December 2010

The good weights for the one-sided Hardy-Littlewood operators have been characterized by conditions . In this paper we introduce a new condition which is analogous to A∞. We show several characterizations of . For example, we prove that the class of weights is the union of classes. We also give a new characterization of weights. Finally, as an application of condition, we characterize the weights for one-sided fractional integrals and one-sided fractional maximal operators.
Homomorphisms of Distributive Lattices as Restrictions of Congruences. II. Planarity and Automorphisms
Authors: Grätzer G. , Lakser H.
Published: December 2010

We prove that any {0,1 }-preserving homomorphism of finite distributive lattices can be realized as the restriction of the congruence relations of a finite planar lattice with no nontrivial automorphisms to an ideal of that lattice, where this ideal also has no nontrivial automorphisms. We also prove that any {0,1 }-preserving homomorphism of finite distributive lattices with more than one element and any homomorphism of groups can be realized, simultaneously, as the restriction of the congruence relations and, respectively, the restriction of the automorphisms of a lattice L to those of an ideal of L; if the groups are both finite, then so is the lattice L.
Kernel Generated Two-Time Parameter Gaussian Processes and Some of Their Path Properties
Authors: Csörgő Miklós , Lin Zheng-Yan , Shao Qi-Man
Published: December 2010

We study path properties of kernel generated two-time parameter, not necessarily stationary, Gaussian processes. We establish large deviation results for some increments of these processes and use these results to prove some of their moduli of continuity and other path properties.
Operator Algebras with Contractive Approximate Identities
Authors: Poon Yiu-Tung , Ruan Zhong-Jin
Published: December 2010

We study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.
Diffusion on Lie Groups
Authors: Varopoulos N. TH.
Published: December 2010

The heat kernel of an amenable Lie group satisfies either pt ~ exp(—ct1/3) or pt ~ t-a as t → ∞. We give a condition on the Lie algebra which characterizes the two cases.
Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs
Authors: Lancaster P. , Rodman L.
Published: December 2010

Real matrix pairs (A,H) satisfying det H ≠ 0, HT = εH, and HA - ηATH, where ε, η take the values +1 or —1, are considered. It is shown that maximal A-invariant H-neutral subspaces have the same dimension (depending on ε and η), called the order of neutrality of the pair (A, H). The order of neutrality of definitizable pairs is investigated. In particular, this concept is used to obtain lower bounds for the number of pure imaginary eigenvalues of low rank perturbations of definitizable pairs when (ε,η) = (1, - 1 ) and when (ε,η) = (—1,—1).
Conjugacy Classes in Algebraic Monoids II
Authors: Putcha Mohan S.
Published: December 2010

Let M be a connected linear algebraic monoid with zero and a reductive unit group. We show that there exist reductive groups G1,..., Gt, each with an automorphism, such that the conjugacy classes of M are in a natural bijective correspondence with the twisted conjugacy classes of Gi, i = 1,..., t.
Exact Inequalities for the Norms of Factors of Polynomials
Authors: Borwein Peter B.
Published: December 2010

This paper addresses a number of questions concerning the size of factors of polynomials. Let p be a monic algebraic polynomial of degree n and suppose q1q2 … qi is a monic factor of p of degree m. Then we can, in many cases, exactly determine

Here ‖ . ‖ is the supremum norm either on [—1, 1] or on {|z| ≤ 1}. We do this by showing that, in the interval case, for each m and n, the n-th Chebyshev polynomial is extremal. This extends work of Gel'fond, Mahler, Granville, Boyd and others. A number of variants of this problem are also considered.
Simplicity Of Reduced Amalgamated Products of C*-Algebras
Authors: McClanahan Kevin
Published: December 2010

We give sufficient conditions for the simplicity of reduced amalgamated products of C*-algebras. We show that in some situations a minimal projection in a unital C*-algebra A is minimal in a free product A *-cB. We show that in certain situations if a minimal projection in A were minimal in a particular reduced free product of A and B then the reduced free product would be a simple C*-algebra which has finite and infinite projections.
Weakly Purely Finitely Additive Measures
Authors: Rüttimann Gottfried T.
Published: December 2010

Let L be an orthomodular poset. A positive measure ξ on L is said to be weakly purely finitely additive if the zero measure is the only completely additive
measure majorized by ξ. It was shown in [15] that, in an arbitrary orthomodular poset L, every positive measures μ is the sum v + ξ of a positive completely additive measure
v and a weakly purely finitely additive measure ξ. We give sufficient conditions for this
Yosida-Hewitt-type decomposition to be unique.

A positive measure λ on L is said to be filtering if every non-zero element p in L majorizes a non-zero element q on which λ vanishes. A filtering measure is weakly purely finitely additive. Filtering measures play a mediator role throughout these investigations since some of the aforementioned conditions are given in terms of these.

The results obtained here are then viewed in the context of Boolean lattices and applied to lattices of idempotents of non-associative JBW-algebras.
On Irreducible Representations of So2n+1 × So2m
Authors: Gross Benedict H. , Prasad Dipendra
Published: December 2010

In this paper, we study the restriction of irreducible representations of the group SO2n+1 × SO2m to a spherical subgroup.
Loops as Invariant Sections in Groups, and their Geometry
Authors: Nagy Péter T. , Strambach Karl
Published: December 2010

We investigate left conjugacy closed loops which can be given by invariant sections in the group generated by their left translations. These loops are generalizations of the conjugacy closed loops introduced in [13] just as Bol loops generalize Moufang loops. The relations of these loops to common classes of loops are studied. For instance on a connected manifold we construct proper topological left conjugacy closed loops satisfying the left Bol condition but show that any differentiable such loop must be a group. We show that the configurational condition in the 3-net corresponding to an isotopy class of left conjugacy closed loops has the same importance in the geometry of 3-nets as the Reidemeister or the Bol condition.
Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator
Authors: Ortega Salvador P.
Published: December 2010

In this paper we characterize weighted Lorentz norm inequalities for the one sided Hardy-Littlewood maximal function

Similar questions are discussed for the maximal operator associated to an invertible measure preserving transformation of a measure space.
The Universal Theory of Ordered Equidecomposability Types Semigroups
Authors: Wehrung Friedrich
Published: December 2010

We prove that a commutative preordered semigroup embeds into the space of all equidecomposability types of subsets of some set equipped with a group action (in short, a full type space) if and only if it satisfies the following axioms: (i) (⩝x,y) (x ≤ x + y); (ii) (⩝x,y)((x ≤ y and y ≤ x) ⇒ x = y); (iii) (⩝x,y,u, v)((x + u ≤ y + u and u ≤ v) ⩝ x + v ≤ y ≤ v); (iv) (⩝x, u, V)((x + u = u and u ≤ v) ⇒ x + v = v); (v) (⩝x,y)(mx ≤ my ⇒ x ≤ y) (all m ∊ Ν \ {0}). Furthermore, such a structure can always be embedded into a reduced power of the space Τ of nonempty initial segments of + with rational (possibly infinite) endpoints, equipped with the addition defined by and the ordering defined by . As a corollary, the set of all universal formulas of (+, ≤) satisfied by all full type spaces is decidable.
Sharpness in Young's Inequality for Convolution Products
Authors: Nielsen Ole A.
Published: December 2010

Suppose that Gis a locally compact group with modular function Δ and that p, q, r are three numbers in the interval (l,∞) satisfying. If cp,q(G) is the smallest constant c such thatfor all functions f, g ∈ Cc(G) (here the convolution product is with respect to left Haar measure andis the exponent which is conjugate to p) then Young's inequality asserts that cp,q(G) ≤ 1. This paper contains three results about these constants. Firstly, if G contains a compact open subgroup then cp,q(G) = 1 and, as an extension of an earlier result of J. J. F. Fournier, it is shown that there is a constant cp,q< 1 such that if G does not contain a compact open subgroup then c<(G) ≤ c≤. Secondly, Beckner's calculation ofis used to obtain the value of cp,q(G) for all simply-connected solvable Lie groups and all nilpotent Lie groups. And thirdly, it is shown that for a nilpotent Lie group the setis not contained in the union of the spaces Ls(G),.
Multipliers on Spaces of Analytic Functions
Authors: Blasco Oscar
Published: December 2010

In the paper we find, for certain values of the parameters, the spaces of multipliers (H(p, q, α), H(s, t, β) and (H(p, q, α), ls), where H(p, q, α) denotes the space of analytic functions on the unit disc such that . As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces.
On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures
Authors: Duran Antonio J.
Published: December 2010

In this paper, we prove that any sequence of polynomials (pn)n for which dgr(pn) = n which satisfies a (2N + l)-term recurrence relation is orthogonal with respect to a positive definite N × N matrix of measures. We use that result to prove asymptotic properties of the kernel polynomials associated to a positive measure or a positive definite matrix of measures. Finally, some examples are given.
The Generalized Wielandt Subgroup of a Group
Authors: Beidleman James C. , Dixon Martyn R. , Robinson Derek J. S.
Published: December 2010

The intersection IW(G) of the normalizers of the infinite subnormal subgroups of a group G is a characteristic subgroup containing the Wielandt subgroup W(G) which we call the generalized Wielandt subgroup. In this paper we show that if G is infinite, then the structure of IW(G)/ W(G) is quite restricted, being controlled by a certain characteristic subgroup S(G). If S(G) is finite, then so is IW(G)/ W(G), whereas if S(G) is an infinite Prüfer-by-finite group, then IW(G)/W(G) is metabelian. In all other cases, IW(G) = W(G).
Thaine's Method for Circular Units and a Conjecture of Gross
Authors: Darmon Henri
Published: December 2010

We formulate a conjecture analogous to Gross' refinement of the Stark conjectures on special values of abelian L-series at s = 0. Some evidence for the conjecture can be obtained, thanks to the fundamental ideas of F. Thaine.
On the Ergodic Averages and the Ergodic Hilbert Transform
Authors: Fernández-Cabrera L. M. , Martín-Reyes F. J. , Torrea J. L.
Published: December 2010

Let T be an invertible measure-preserving transformation on a σ-finite measure space (X, μ) and let 1 < p < ∞. This paper uses an abstract method developed by José Luis Rubio de Francia which allows us to give a unified approach to the problems of characterizing the positive measurable functions v such that the limit of the ergodic averages or the ergodic Hilbert transform exist for all f ∈ Lp(νdμ). As a corollary, we obtain that both problems are equivalent, extending to this setting some results of R. Jajte, I. Berkson, J. Bourgain and A. Gillespie. We do not assume the boundedness of the operator Tf(x) = f(Tx) on Lp(νdμ). However, the method of Rubio de Francia shows that the problems of convergence are equivalent to the existence of some measurable positive function u such that the ergodic maximal operator and the ergodic Hilbert transform are bounded from LP(νdμ) into LP(udμ). We also study and solve the dual problem.
Distance From Projections to Nilpotents
Authors: Macdonald Gordon W.
Published: December 2010

The distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .
On Permutability and Submultiplicativity of Spectral Radius
Authors: Longstaff W. E. , Radjavi H.
Published: December 2010

Let r(T) denote the spectral radius of the operator T acting on a complex Hilbert space H. Let S be a multiplicative semigroup of operators on H. We say that r is permutable on 𝓢 if r(ABC) = r(BAC), for every A,B,C ∈ 𝓢. We say that r is submultiplicative on 𝓢 if r(AB) ≤ r(A)r(B), for every A, B ∈ 𝓢. It is known that, if r is permutable on 𝓢, then it is submultiplicative. We show that the converse holds in each of the following cases: (i) 𝓢 consists of compact operators (ii) 𝓢 consists of normal operators (iii) 𝓢 is generated by orthogonal projections.
Frames and Stable Bases for Shift-Invariant Subspaces of L2(ℝd)
Authors: Ron Amos , Shen Zuowei
Published: December 2010

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator Whenever T is well-defined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L2(ℝd), and for sets X of the form with Φ either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT* and T* T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators.
Metrics of Positive Scalar Curvature on Spherical Space Forms
Authors: Botvinnik Boris , Gilkey Peter B.
Published: December 2010

We use the eta invariant to show every non-simply connected spherical space form of dimension m ≥ 5 has a countable family of non bordant metrics of positive scalar curvature.
Solvability of Some Singular Boundary Value Problems on the Semi-Infinite Interval
Authors: O'Regan Donal
Published: December 2010

Existence of solutions to the nonlinear boundary value problem on the semi-infinite interval bounded on [0, ∞), are established. In the process we obtain new existence results for boundary value problems on compact intervals.
On the Recovery of Analytic Functions
Authors: Cima Joseph A. , Stessin Michael
Published: December 2010

In this paper we consider questions of recapturing an analytic function in a Banach space from its values on a uniqueness set. The principal method is to use reproducing kernels to construct a sequence in the Banach space which converges in norm to the given functions. The method works for several classical Banach spaces of analytic functions including some Hardy and Bergman spaces.
Dade's Conjecture for Chevalley Groups G2(q) in Non-Defining Characteristics
Authors: An Jianbei , Gao Yun
Published: December 2010

This paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups of Lie type. The local structures of certain radical chains of Chevalley groups of type G2 are given and the ordinary conjecture is confirmed for the groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.
Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights
Authors: Damelin S. B. , Lubinsky D. S.
Published: December 2010

We investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn(W2, x) for Erdös 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 < ∞, Δ ∊ ℝ, k > 0. 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
First Order Operators on Manifolds With a Group Action
Authors: Fegan H. D. , Steer B.
Published: December 2010

We investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.
Forbidden Subcategories of Non-Polynomial Growth Tame Simply Connected Algebras
Authors: De La Peña J. A. , Skowroński A.
Published: December 2010

Let k be an algebraically closed field and A = kQ/I be a basic finite dimensional k-algebra such that Q is a connected quiver without oriented cycles. Assume that A is strongly simply connected, that is, for every convex subcategory B of A the first Hochschild cohomology H1(B, B) vanishes. The algebra A is sincere if it admits an indecomposable module having all simples as composition factors. We study the structure of strongly simply connected sincere algebras of tame representation type. We show that a sincere, tame, strongly connected algebra A which contains a convex subcategory which is either representation-infinite tilted of type Ẽp, p = 6,7,8, or a tubular algebra, is of polynomial growth.
Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups
Authors: Kapovich Ilya , Short Hamish
Published: December 2010

Analogues of a theorem of Greenberg about finitely generated subgroups of free groups are proved for quasiconvex subgroups of word hyperbolic groups. It is shown that a quasiconvex subgroup of a word hyperbolic group is a finite index subgroup of only finitely many other subgroups.
The Residual Spectrum ofG2
Authors: Kim Henry H.
Published: December 2010

We completely determine the residual spectrum of the split exceptional group of typeG2, thus completing the work of Langlands and Moeglin-Waldspurger on the part of the residual spectrum attached to the trivial character of the maximal torus. We also give the Arthur parameters for the residual spectrum coming from Borel subgroups. The interpretation in terms of Arthur parameters explains the “bizarre” multiplicity condition in Moeglin-Waldspurger's work. It is related to the fact that the component group of the Arthur parameter is non-abelian.
Compactness of a Locally Compact Group G and Geometric Properties of Ap(G)
Authors: Miao Tianxuan
Published: December 2010

Let G be a locally compact topological group. A number of characterizations are given of the class of compact groups in terms of the geometric properties such as Radon-Nikodym property, Dunford-Pettis property and Schur property of Ap(G), and the properties of the multiplication operator on PFp(G). We extend and improve several results of Lau and Ülger [17] to Ap(G) and Bp(G) for arbitrary p.
Sufficiently Homogeneous Closed Embeddings of 𝔸n-1 into 𝔸n are Linear
Authors: Russell Peter
Published: December 2010

We show that over a field k of characteristic zero an affine (n — 1)- space embedded as a closed subvariety in affine n-space and homogeneous for a codimension two linear torus action on is defined by the vanishing of a variable.
Automorphisms of the Lie Algebras W* in Characteristic 0
Authors: Osborn J. Marshall
Published: December 2010

In a recent paper [2] we defined four classes of infinite dimensional simple Lie algebras over a field of characteristic 0 which we called W*, S*, H*, and K*. As the names suggest, these classes generalize the Lie algebras of Cartan type. A second paper [3] investigates the derivations of the algebras W* and S*, and the possible isomorphisms between these algebras and the algebras defined by Block [1]. In the present paper we investigate the automorphisms of the algebras of type W*.
Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
Authors: Xu Yuan
Published: December 2010

Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions |x1|α1 . . . |xd|αd on the unit sphere Sd-1 in ℝd. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator.
Some Summation Theorems and Transformations for Q-Series
Authors: Ismail Mourad E. H. , Rahman Mizan , Suslov Sergei K.
Published: December 2010

We introduce a double sum extension of a very well-poised series and extend to this the transformations of Bailey and Sears as well as the 6ϕ5 summation formula of F. H. Jackson and the q-Dixon sum. We also give q-integral representations of the double sum. Generalizations of the Nassrallah-Rahman integral are also found.
The Schreier Technique for Subalgebras of a Free Lie Algebra
Authors: Rosset Shmuel , Wasserman Alon
Published: December 2010

In group theory Schreier's technique provides a basis for a subgroup of a free group. In this paper an analogue is developed for free Lie algebras. It hinges on the idea of cutting a Hall set into two parts. Using it, we show that proper subalgebras of finite codimension are not finitely generated and, following M. Hall, that a finitely generated subalgebra is a free factor of a subalgebra of finite codimension.
Fine Spectra and Limit Laws, II First-Order 0–1 Laws
Authors: Burris Stanley , Kevin Compton  , Odlyzko Andrew , Richmond Bruce
Published: December 2010

Using Feferman-Vaught techniques a condition on the fine spectrum of an admissible class of structures is found which leads to a first-order 0–1 law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first–order 0–1 law.

If the condition is satisfied (and hence we have a first-order 0–1 law) we give a natural model of the limit law theory; and show that the limit law theory is decidable if the theory of the directly indecomposables is decidable. Using asymptotic methods from the partition calculus a useful test is derived to show several admissible classes have a first–order 0–1 law.
On q-Carleson Measures for Spaces of M-Harmonic Functions
Authors: Cascante Carme , Ortega Joaquin M.
Published: December 2010

In this paper we study the q-Carleson measures for a space of M-harmonic potentials in the unit ball of Cn, when q < p. We obtain some computable sufficient conditions, and study the relations among them.
Finite Dimensional Representations of Ut(sl (2)) at Roots of Unity
Authors: Jie Xiao
Published: December 2010

All finite dimensional indecomposable representations of Ut(Sl (2)) at roots of 1 are determined.
Boundedness of Solutions of Parabolic Equations With Anisotropic Growth Conditions
Authors: Mingqi Yu , Xiting Lian
Published: December 2010

In this paper, we consider the parabolic equation with anisotropic growth conditions, and obtain some criteria on boundedness of solutions, which generalize the corresponding results for the isotropic case.
The Zero Distribution of Orthogonal Rational Functions on the Unit Circle
Authors: Pan K.
Published: December 2010

Rational functions orthogonal on the unit circle with prescribed poles lying outside the unit circle are studied. We use the potential theory to discuss the zeros distribution for the orthogonal rational functions.
Rational Classification of Simple Function Space Components for Flag Manifolds
Authors: Smith Samuel Bruce
Published: December 2010

LetM(X, Y) denote the space of all continuous functions between X and Y and Mƒ(X, Y) the path component corresponding to a given map ƒ : X → Y. When X and Y are classical flag manifolds, we prove the components of M(X, Y) corresponding to “simple” maps ƒ are classified up to rational homotopy type by the dimension of the kernel of ƒ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.
Proof of a Conjecture of Goulden and Jackson
Authors: Okounkov Andrei
Published: December 2010

We prove an integration formula involving Jack polynomials conjectured by I. P. Goulden and D.M. Jackson in connection with enumeration of maps in surfaces.
Polynomials With {0, +1, -1} Coefficients and a Root Close to a Given Point
Authors: Borwein Peter , Pinner Christopher
Published: December 2010

For a fixed algebraic number α we discuss how closely α can be approximated by a root of a {0, +1, -1} polynomial of given degree. We show that the worst rate of approximation tends to occur for roots of unity, particularly those of small degree. For roots of unity these bounds depend on the order of vanishing, k, of the polynomial at α.

In particular we obtain the following. Let BN denote the set of roots of all {0, +1, -1} polynomials of degree at most N and BN(α k) the roots of those polynomials that have a root of order at most k at α. For a Pisot number α in (1, 2] we show that

and for a root of unity α that

We study in detail the case of α = 1, where, by far, the best approximations are real. We give fairly precise bounds on the closest real root to 1. When k = 0 or 1 we can describe the extremal polynomials explicitly.
Quantization of the 4-Dimensional Nilpotent Orbit of Sl(3, ℝ)
Authors: Brylinski Ranee
Published: December 2010

We give a new geometric model for the quantization of the 4-dimensional conical (nilpotent) adjoint orbit Oℝof SL(3,ℝ). The space of quantization is the space of holomorphic functions on 𝕔2- {0}) which are square integrable with respect to a signed measure defined by a Meijer G-function. We construct the quantization out a non-flat Kaehler structure on 𝕔2- {0}) (the universal cover of Oℝ) with Kaehler potential ρ |z|4.
The Von Neumann Algebra VN(G) of a Locally Compact Group and Quotients of Its Subspaces
Authors: Hu Zhiguo
Published: December 2010

Let VN(G) be the von Neumann algebra of a locally compact group G. We denote by μ the initial ordinal with |μ| equal to the smallest cardinality of an open basis at the unit of G and X = ﹛α ; α < μ﹜.We show that if G is nondiscrete then there exist an isometric *-isomorphism of l∞(X) into VN(G) and a positive linear mapping π of VN(G) onto l∞(X) such that π o = idl∞(X) and and π have certain additional properties. Let UCB((Ĝ)) be the C*–algebra generated by operators in VN(G) with compact support and F(Ĝ) the space of all T∈ VN(G) such that all topologically invariant means on VN(G) attain the same value at T. The construction of the mapping π leads to the conclusion that the quotient space UCB((Ĝ))/F((Ĝ)) ∪UCB((Ĝ)) has l∞(X) as a continuous linear image if G is nondiscrete. When G is further assumed to be non-metrizable, it is shown that UCB((Ĝ))/F((Ĝ)) ∪UCB((Ĝ)) contains a linear isomorphic copy of l∞(X). Similar results are also obtained for other quotient spaces.
Subalgebras Which Appear in Quantum Iwasawa Decompositions
Authors: Letzter Gail
Published: December 2010

Let g be a semisimple Lie algebra. Quantum analogs of the enveloping algebra of the fixed Lie subalgebra are introduced for involutions corresponding to the negative of a diagram automorphism. These subalgebras of the quantized enveloping algebra specialize to their classical counterparts. They are used to form an Iwasawa type decompostition and begin a study of quantum Harish-Chandra modules.
Elementary Proof of the Fundamental Lemma For a Unitary Group
Authors: Flicker Yuval Z.
Published: December 2010

The fundamental lemma in the theory of automorphic forms is proven for the (quasi-split) unitary group U(3) in three variables associatedwith a quadratic extension of p-adic fields, and its endoscopic group U(2), by means of a new, elementary technique. This lemma is a prerequisite for an application of the trace formula to classify the automorphic and admissible representations of U(3) in terms of those of U(2) and base change to GL(3). It compares the (unstable) orbital integral of the characteristic function of the standard maximal compact subgroup K of U(3) at a regular element (whose centralizer T is a torus), with an analogous (stable) orbital integral on the endoscopic group U(2). The technique is based on computing the sum over the double coset space T\G/K which describes the integral, by means of an intermediate double coset space H\G/K for a subgroup H of G= U(3) containing T. Such an argument originates from Weissauer's work on the symplectic group. The lemma is proven for both ramified and unramified regular elements, for which endoscopy occurs (the stable conjugacy class is not a single orbit).
Inequalities for Rational Functions With Prescribed Poles
Authors: Min G.
Published: December 2010

This paper considers the rational system Pn(a1, a2,……,an) := with nonreal elements in paired by complex conjugation. It gives a sharp (to constant) Markov-type inequality for real rational functions in Pn(a1, a2,……an). The corresponding Markov-type inequality for high derivatives is established, as well as Nikolskii-type inequalities. Some sharp Markov- and Bernstein-type inequalities with curved majorants for rational functions in Pn(a1, a2,……an) are obtained, which generalize some results for the classical polynomials. A sharp Schur-type inequality is also proved and plays a key role in the proofs of our main results
Units in Group Rings of Free Products of Prime Cyclic Groups
Authors: Dokuchaev Michael A. , Sobral Singer Maria Lucia
Published: December 2010

Let G be a free product of cyclic groups of prime order. The structure of the unit group U(ℚG) of the rational group ring ℚG is given in terms of free products and amalgamated free products of groups. As an application, all finite subgroups of U(ℚG), up to conjugacy, are described and the Zassenhaus Conjecture for finite subgroups in ℤ G is proved. A strong version of the Tits Alternative for U(ℚG) is obtained as a corollary of the structural result.
The Groups of the Regular Star-Polytopes
Authors: McMullen Peter
Published: December 2010

The regular star-polyhedron is isomorphic to the abstract polyhedron {5, 5,| 3}, where the last entry “3” in its symbol denotes the size of a hole, given by the imposition of a certain extra relation on the group of the hyperbolic honeycomb {5, 5}. Here, analogous formulations are found for the groups of the regular 4-dimensional star-polytopes, and for those of the non-discrete regular 4-dimensional honeycombs. In all cases, the extra group relations to be imposed on the corresponding Coxeter groups are those arising from “deep holes”; thus the abstract description of for k = 1 or 2. The non-discrete quasi-regular honeycombs in 𝔼3, on the other hand, are not determined in an analogous way.
Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions
Authors: Froese Richard
Published: December 2010

The purpose of this note is to provide a simple proof of the sharp polynomial upper bound for the resonance counting function of a Schrödinger operator in odd dimensions. At the same time we generalize the result to the class of superexponentially decreasing potentials.
Multipliers of Fractional Cauchy Transforms and Smoothness Conditions
Authors: Luo Donghan , Macgregor Thomas
Published: December 2010

This paper studies conditions on an analytic function that imply it belongs to Mα, the set of multipliers of the family of functions given by where μ is a complex Borel measure on the unit circle and α > 0. There are two main theorems. The first asserts that if 0 < α < 1 and sup. The second asserts that if 0 < α < 1, ƒ ∈ H∞ and supt. The conditions in these theorems are shown to relate to a number of smoothness conditions on the unit circle for a function analytic in the open unit disk and continuous in its closure.
Fractals in the Large
Authors: Strichartz Robert S.
Published: December 2010

A reverse iterated function system (r.i.f.s.) is defined to be a set of expansive maps ﹛T1,…, Tm﹜ on a discrete metric space M. An invariant set F is defined to be a set satisfying , and an invariant measure μ is defined to be a solution of for positive weights pj. The structure and basic properties of such invariant sets and measures is described, and some examples are given. A blowup ℱ of a self-similar set F in ℝn is defined to be the union of an increasing sequence of sets, each similar to F. We give a general construction of blowups, and show that under certain hypotheses a blowup is the sum set of F with an invariant set for a r.i.f.s. Some examples of blowups of familiar fractals are described. If μ is an invariant measure on ℤ+ for a linear r.i.f.s., we describe the behavior of its analytic transform, the power series on the unit disc.
Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2
Authors: Symesak Frédéric
Published: December 2010

The aimof this paper is to study small Hankel operatorshon the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbolƒso thathbelongs to the Schatten classSp, 1 ≤p< +∞.
Tableaux Realization of Generalized Verma Modules
Authors: Mazorchuk Volodymyr
Published: December 2010

We construct the tableaux realization of generalized Verma modules over the Lie algebrasl(3, ℂ). By the same procedure we construct and investigate the structure of a new family of generalized Verma modules oversl(n, ℂ).
Decomposition Varieties in Semisimple Lie Algebras
Authors: Broer Abraham
Published: December 2010

The notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements.

We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, e.g., its normalization has rational singularities.

The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.
Ward’s Solitons II: Exact Solutions
Authors: Anand Christopher Kumar
Published: December 2010

In a previous paper, we gave a correspondence between certain exact solutions to a (2 + 1)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions.
A Lower Bound For KxL Of Quasi-Polarized Surfaces (X, L) With Non-Negative Kodaira Dimension
Authors: Fukuma Yoshiaki
Published: December 2010

Let X be a smooth projective surface over the complex number field and let L be a nef-big divisor on X. Here we consider the following conjecture; If the Kodaira dimension ≥ 0, then KXL ≥ 2q(X) - 4, where q(X) is the irregularity of X. In this paper, we prove that this conjecture is true if (1) the case in which = 0 or 1, (2) the case in which = 2 and h0(L) ≥ 2, or (3) the case in which = 2, X is minimal, h0(L) = 1, and L satisfies some conditions.
The Dual Pair G2 × PU3 (D) (p-Adic Case)
Authors: Savin Gordan , Gan Wee Teck
Published: December 2010

We study the correspondence of representations arising by restricting the minimal representation of the linear group of type E7 and relative rank 4. The main tool is computations of the Jacquet modules of the minimal representation with respect to maximal parabolic subgroups of G2 and PU3(D).
Poles of Siegel Eisenstein Series on U(n, n)
Authors: Tan Victor
Published: December 2010

Let U(n, n) be the rank n quasi-split unitary group over a number field. We show that the normalized Siegel Eisenstein series of U(n, n) has at most simple poles at the integers or half integers in certain strip of the complex plane.