bluuebunny/crossref_metadata_2025 huggingface dataset:
New Almost Periodic Type Functions and Solutions of Differential Equations
Authors: Basit Bolis , Zhang Chuanyi
Published: December 2010

Let X be a Banach space and . Let Π and Π0 be two subspaces of , the Banach space of bounded continuous functions from 𝕁 to X. We seek conditions under which Π + Π0 is closed in . This led to introduce a general space, which contains many classes of almost periodic type functions as subspaces. We prove some recent results on indefinite integral for the elements of these classes. We apply certain results on harmonic analysis to investigate solutions of differential equations. As an application we study specific spaces: the spaces of asymptotic and pseudo almost automorphic functions and their solutions of some ordinary quasi-linear and a non-linear parabolic partial differential equations.
Markov's Theorem for Orthogonal Matrix Polynomials
Authors: Duran Antonio J.
Published: December 2010

Markov's Theorem shows asymptotic behavior of the ratio between the n-th orthonormal polynomial with respect to a positive measure and the n-th polynomial of the second kind. In this paper we extend Markov's Theorem for orthogonal matrix polynomials.
Multiplication Invariant Subspaces of Hardy Spaces
Authors: Lance T. L. , Stessin M. I.
Published: December 2010

This paper studies closed subspaces L of the Hardy spaces Hp which are g-invariant (i.e., g. L ⊆ L) where g is inner, g ≠ 1. If p = 2, theWold decomposition theorem implies that there is a countable “g-basis” f1, f2, . . . of L in the sense that L is a direct sum of spaces fj . H2[g] where H2[g] = {f o g | f ∈ H2}. The basis elements fj satisfy the additional property that ∫T |fj|2gk = 0, k = 1, 2, . . . . We call such functions g-2-inner. It also follows that any f ∈ H2 can be factored f = hf ,2 . (F2 o g) where hf,2 is g-2-inner and F is outer, generalizing the classical Riesz factorization. Using Lp estimates for the canonical decomposition of H2,we find a factorization f = hf ,p.(Fpog) for f ∈ Hp. If p ≤ 1 and g is a finite Blaschke product we obtain, for any g-invariant L ⊆ Hp, a finite g-basis of g-p-inner functions.
Differential Equations Defined by the Sum of two Quasi-Homogeneous Vector Fields
Authors: Coll B. , Gasull A. , Prohens R.
Published: December 2010

In this paper we prove, that under certain hypotheses, the planar differential equation: ˙x = X1(x, y) + X2(x, y), ˙y = Y1(x, y) + Y2(x, y), where (Xi, Yi), i = 1, 2, are quasi-homogeneous vector fields, has at most two limit cycles. The main tools used in the proof are the generalized polar coordinates, introduced by Lyapunov to study the stability of degenerate critical points, and the analysis of the derivatives of the Poincar´e return map. Our results generalize those obtained for polynomial systems with homogeneous non-linearities.
On Hurwitz Constants for Fuchsian Groups
Authors: Vulakh L. Ya.
Published: December 2010

Explicit bounds for the Hurwitz constants for general cofinite Fuchsian groups have been found. It is shown that the bounds obtained are exact for the Hecke groups and triangular groups with signature (0 : 2, p, q).
A Counterexample in Lp Approximation by Harmonic Functions
Authors: Mateu Joan
Published: December 2010

For we show that the conditions for all open sets G, C2,q denoting Bessel capacity, are not sufficient to characterize the compact sets X with the property that each function harmonic on and in Lp(X) is the limit in the Lp norm of a sequence of functions which are harmonic on neighbourhoods of X.
On the Zeros of Some Genus Polynomials
Authors: Stahl Saul
Published: December 2010

In the genus polynomial of the graph G, the coefficient of xk is the number of distinct embeddings of the graph G on the oriented surface of genus k. It is shown that for several infinite families of graphs all the zeros of the genus polynomial are real and negative. This implies that their coefficients, which constitute the genus distribution of the graph, are log concave and therefore also unimodal. The geometric distribution of the zeros of some of these polynomials is also investigated and some new genus polynomials are presented.
Dilations of one Parameter Semigroups of Positive Contractions on Lp Spaces
Authors: Fendler Gero
Published: December 2010

It is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an Lp-space, for 1 < p < ∞ p ≠ 2, can be dilated by a strongly continuous group of (sub)positive isometries in a manner analogous to the dilation M. A. Akçoglu and L. Sucheston constructed for a discrete semigroup of (sub)positive contractions. From this an improvement of a von Neumann type estimation, due to R. R.Coifman and G.Weiss, on the transfer map belonging to the semigroup is deduced.
Trace Functions in the Ring of Fractions of Polycyclic Group Rings, II
Authors: Lichtman A. I.
Published: December 2010

We prove the existence of trace functions in the rings of fractions of polycyclic-by-finite group rings or their homomorphic images. In particular a trace function exists in the ring of fractions of KH, where H is a polycyclic-by-finite group and char K > N, where N is a constant depending on H.
Approximation by Multiple Refinable Functions
Authors: Jia R. Q. , Riemenschneider S. D. , Zhou D. X.
Published: December 2010

We consider the shift-invariant space, 𝕊(Φ), generated by a set Φ = {Φ1,..., Φr} of compactly supported distributions on R when the vector of distributions ϕ:= {Φ1,..., Φr} T satisfies a system of refinement equations expressed in matrix form as

where a is a finitely supported sequence of r x r matrices of complex numbers. Such multiple refinable functions occur naturally in the study of multiple wavelets.

The purpose of the present paper is to characterize the accuracy of Φ, the order of the polynomial space contained in 𝕊(Φ), strictly in terms of the refinement mask a. The accuracy determines the Lp-approximation order of 𝕊(Φ) when the functions in (Φ) belong to Lp(ℝ) (see Jia [10]). The characterization is achieved in terms of the eigenvalues and eigenvectors of the subdivision operator associated with the mask a. In particular, they extend and improve the results of Heil, Strang and Strela [7], and of Plonka [16]. In addition, a counterexample is given to the statement of Strang and Strela [20] that the eigenvalues of the subdivision operator determine the accuracy. The results do not require the linear independence of the shifts of Φ.
Majorations Effectives Pour L’ Équation de Fermat Généralisée
Authors: Kraus Alain
Published: December 2010

Soient A, B et C trois entiers non nuls premiers entre eux deux à deux, et p un nombre premier. Comme conséquence des travaux de A. Wiles et F. Diamond sur la conjecture de Taniyama-Weil, on explicite une constante f(A, B, C) telle que, sous certaines conditions portant sur A, B et C, l’équation Axp+ Byp+ Czp= 0 n’a aucune solution non triviale dans ℤ, si p est > f(A, B, C). On démontre par ailleurs, sans condition supplémentaire portant sur A, B et C, que cette équation n’a aucune solution non triviale dans ℤ, si p divise xyz, et si p est > f(A, B,C).
1-Complemented Subspaces of Spaces With 1-Unconditional Bases
Authors: Randrianantoanina Beata
Published: December 2010

We prove that if X is a complex strictly monotone sequence space with 1-unconditional basis, Y ⊆ X has no bands isometric to ℓ22 and Y is the range of norm-one projection from X, then Y is a closed linear span a family of mutually disjoint vectors in X.

We completely characterize 1-complemented subspaces and norm-one projections in complex spaces ℓp(ℓq) for 1 ≤ p,q > ∞.

Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are 1-complemented in (real or complex) Orlicz or Lorentz sequence spaces. In particular if an Orlicz or Lorentz space X is not isomorphic to ℓp for some 1 ≤ p,q > ∞ then the only subspaces of X which are 1-complemented and disjointly supported are the closed linear spans of block bases with constant coefficients.
Hecke Algebras and Class-Group Invariants
Authors: Snaith V. P.
Published: December 2010

Let G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, ψ, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]). Alternative constructions of Chinburg invariants arising fromthe Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of ψ. As an application we show that two such constructions coincide.
The Explicit Solution of the -Neumann Problem in a Non-Isotropic Siegel Domain
Authors: Tie Jingzhi
Published: December 2010

In this paper, we solve the-Neumann problem on (0, q) forms, 0 ≤ q ≤ n, in the strictly pseudoconvex non-isotropic Siegel domain:where aj> 0 for j = 1,2, . . . , n. The metric we use is invariant under the action of the Heisenberg group on the domain. The fundamental solution of the related differential equation is derived via the Laguerre calculus. We obtain an explicit formula for the kernel of the Neumann operator. We also construct the solution of the corresponding heat equation and the fundamental solution of the Laplacian operator on the Heisenberg group.
Intégration Du Sous-Différentiel Proximal: Un Contre Exemple
Authors: Benoist Joël
Published: December 2010

Etant donnée une partie D dénombrable et dense de ℝ, nous construisons une infinité de fonctions Lipschitziennes définies sur ℝ, s’annulant en zéro, dont le sous-différentiel proximal est égal à ]–1, 1[ en tout point de D et est vide en tout point du complémentaire de D. Nous déduisons que deux fonctions dont la différence n’est pas constante peuvent avoir les mêmes sous-différentiels.
Some Norms on Universal Enveloping Algebras
Authors: Gross Leonard
Published: December 2010

The universal enveloping algebra,U(𝔤), of a Lie algebra 𝔤 supports some norms and seminorms that have arisen naturally in the context of heat kernel analysis on Lie groups. These norms and seminorms are investigated here from an algebraic viewpoint. It is shown that the norms corresponding to heat kernels on the associated Lie groups decompose as product norms under the natural isomorphism. The seminorms corresponding to Green's functions are examined at a purely Lie algebra level for sl (2, ℂ). It is also shown that the algebraic dual spaceU′ is spanned by its finite rank elements if and only if 𝔤 is nilpotent.
Hardy Spaces of Conjugate Systems of Temperatures
Authors: Martha Guzmán-Partida  , Pérez-Esteva Salvador
Published: December 2010

We define Hardy spaces of conjugate systems of temperature functions on ℝn+1+ . We show that their boundary distributions are the same as the boundary distributions of the usual Hardy spaces of conjugate systems of harmonic functions.
Unbounded Fredholm Modules and Spectral Flow
Authors: Carey Alan , Phillips John
Published: December 2010

An odd unbounded (respectively, p-summable) Fredholm module for a unital Banach *-algebra, A, is a pair (H,D) where A is represented on the Hilbert space, H, and D is an unbounded self-adjoint operator on H satisfying:

(1) (1 + D2)-1 is compact (respectively, Trace_(1 + D2)-(p/2)_∞), and

(2) ﹛a ∈ A | [D, a] is bounded﹜ is a dense *- subalgebra of A.

If u is a unitary in the dense *-subalgebra mentioned in (2) then

uDu* = D + u[D, u*] = D + B

where B is a bounded self-adjoint operator. The path

is a “continuous” path of unbounded self-adjoint “Fredholm” operators. More precisely, we show that

is a norm-continuous path of (bounded) self-adjoint Fredholm operators. The spectral flow of this path is roughly speaking the net number of eigenvalues that pass through 0 in the positive direction as t runs from 0 to 1. This integer,

recovers the pairing of the K-homology class [D] with the K-theory class [u].

We use I.M. Singer's idea (as did E. Getzler in the θ-summable case) to consider the operator B as a parameter in the Banach manifold, Bsa(H), so that spectral flow can be exhibited as the integral of a closed 1-formon this manifold. Now, for B in ourmanifold, any X ∈ TB_Bsa(H)_ is given by an X in Bsa(H) as the derivative at B along the curve t→ B + tX in the manifold. Then we show that for m a sufficiently large half-integer:

is a closed 1-form. For any piecewise smooth path {Dt = D + Bt} with D0 and D1 unitarily equivalent we show that

the integral of the 1-form ã. If D0 and D1 are not unitarily equivalent, wemust add a pair of correction terms to the right-hand side. We also prove a bounded finitely summable version of the form:

for an integer. The unbounded case is proved by reducing to the bounded case via the map . We prove simultaneously a type II version of our results.
Trace Class Elements and Cross-Sections in Kac-Moody Groups
Authors: Brüchert Gerd
Published: December 2010

Let G be an affine Kac-Moody group, π0, … ,πr, πδ its fundamental irreducible representations and χ0, … , χr, χδ their characters. We determine the set of all group elements x such that all πi(x) act as trace class operators, i.e., such that χi(x) exists, then prove that the χ i are class functions. Thus, χ := (χ0, … , χr, χδ) factors to an adjoint quotient χ for G. In a second part, following Steinberg, we define a cross-section C for the potential regular classes in G. We prove that the restriction χ|C behaves well algebraically. Moreover, we obtain an action of C ℂ✗ on C, which leads to a functional identity for χ|C which shows that χ|C is quasi-homogeneous.
Localization Theories for Simplicial Presheaves
Authors: Goerss P. G. , Jardine J. F.
Published: December 2010

Most extant localization theories for spaces, spectra and diagrams of such can be derived from a simple list of axioms which are verified in broad generality. Several new theories are introduced, including localizations for simplicial presheaves and presheaves of spectra at homology theories represented by presheaves of spectra, and a theory of localization along a geometric topos morphism. The ƒ-localization concept has an analog for simplicial presheaves, and specializes to the 𝔸1-local theory of Morel-Voevodsky. This theory answers a question of Soulé concerning integral homology localizations for diagrams of spaces.
Sur les Transformées de Riesz sur les Groupes de Lie Moyennables et sur Certains Espaces Homogènes
Authors: Noël Lohoué  , Mustapha Sami
Published: December 2010

Let Δ be a left invariant sub-Laplacian on a Lie group G and let ▽ be the associated gradient. In this paper we investigate the boundness of the Riesz transform ▽Δ-1/2 on Lie groups G which are amenable and with exponential volume growth and on certain homogenous spaces.
Tempered Representations and the Theta Correspondence
Authors: Roberts Brooks
Published: December 2010

Let V be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field F of characteristic zero, and let n be a nonnegative integer. Suppose that σ ∈ Irr (O(V)) and π ∈ Irr (Sp(n, F)) correspond under the theta correspondence. Assuming that õ is tempered, we investigate the problem of determining the Langlands quotient data for π.
Isomorphism Problem for Metacirculant Graphs of Order a Product of Distinct Primes
Authors: Dobson Edward
Published: December 2010

In this paper, we solve the isomorphism problem for metacirculant graphs of order pq that are not circulant. To solve this problem, we first extend Babai’s characterization of the CI-property to non-Cayley vertex-transitive hypergraphs. Additionally, we find a simple characterization of metacirculant Cayley graphs of order pq, and exactly determine the full isomorphism classes of circulant graphs of order pq.
The Behaviour of Legendre And Ultraspherical Polynomials in Lp-Spaces
Authors: Kalton N. J. , Tzafriri L.
Published: December 2010

We consider the analogue of the λ(p)problem for subsets of the Legendre polynomials or more general ultraspherical polynomials. We obtain the “best possible” result that if 2 < p < 4 then a random subset of N Legendre polynomials of size N4/p-1 spans an Hilbertian subspace. We also answer a question of König concerning the structure of the space of polynomials of degree n in various weighted Lp-spaces.
Imprimitively Generated Lie-Algebraic Hamiltonians and Separation of Variables
Authors: Milson Robert
Published: December 2010

Turbiner’s conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture is given in those cases where the generating Lie-algebra acts imprimitively. The general form of the conjecture is false. A counter-example is given based on the trigonometric Olshanetsky-Perelomov potential corresponding to the A2 root system.
Convergence of Subdifferentials of Convexly Composite Functions
Authors: Combari C. , Poliquin R. , Thibault L.
Published: December 2010

In this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.
Symmetric sequence subspaces of C(α), II
Authors: Leung Denny H. , Tang Wee-Kee
Published: December 2010

If α is an ordinal, then the space of all ordinals less than or equal to α is a compact Hausdorff space when endowed with the order topology. Let C(α) be the space of all continuous real-valued functions defined on the ordinal interval [0; α]. We characterize the symmetric sequence spaces which embed into C(α) for some countable ordinal α. A hierarchy (Eα) of symmetric sequence spaces is constructed so that, for each countable ordinal α, Eα embeds into C(ωωα), but does not embed into C(ωωβ) for any β < α.
Representations of Virasoro-Heisenberg Algebras and Virasoro-Toroidal Algebras
Authors: Fabbri Marc A. , Okoh Frank
Published: December 2010

Virasoro-toroidal algebras, , are semi-direct products of toroidal algebras and the Virasoro algebra. The toroidal algebras are, in turn, multi-loop versions of affine Kac-Moody algebras. Let Γ be an extension of a simply laced lattice by a hyperbolic lattice of rank two. There is a Fock space V(Γ) corresponding to Γ with a decomposition as a complex vector space: V(Γ) = . Fabbri and Moody have shown that when m ≠ 0, K(m) is an irreducible representation of . In this paper we produce a filtration of -submodules of K(0). When L is an arbitrary geometric lattice and n is a positive integer, we construct a Virasoro-Heisenberg algebra . Let Q be an extension of by a degenerate rank one lattice. We determine the components of V(Γ) that are irreducible -modules and we show that the reducible components have a filtration of -submodules with completely reducible quotients. Analogous results are obtained for . These results complement and extend results of Fabbri and Moody.
First Occurrence for the Dual Pairs (U(p, q), U(r, s))
Authors: Paul Annegret
Published: December 2010

We prove a conjecture of Kudla and Rallis about the first occurrence in the theta correspondence, for dual pairs of the form (U(p, q), U(r, s)) and most representations.
Nilpotency of Some Lie Algebras Associated with p-Groups
Authors: Shumyatsky Pavel
Published: December 2010

Let L = L0 + L1 be a 2-graded Lie algebra over a commutative ring with unity in which 2 is invertible. Suppose that L0 is abelian and L is generated by finitely many homogeneous elements a1,...,ak such that every commutator in a1,...,ak is ad-nilpotent. We prove that L is nilpotent. This implies that any periodic residually finite 2ʹ-group G admitting an involutory automorphism ϕ with CG(ϕ) abelian is locally finite.
Brownian Motion and Harmonic Analysis on Sierpinski Carpets
Authors: Barlow Martin T. , Bass Richard F.
Published: December 2010

We consider a class of fractal subsets ofdformed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusionXand determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.
A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type
Authors: Hall Brian C.
Published: December 2010

I consider a two-parameter familyBs,tof unitary transforms mapping anL2-space over a Lie group of compact type onto a holomorphicL2-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with B. Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting casess→ ∞ ands→t/2.
Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers
Authors: Balogh Zoltán M. , Leuenberger Christoph
Published: December 2010

Consider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.
On Limit Multiplicities for Spaces of Automorphic Forms
Authors: Deitmar Anton , Hoffmann Werner
Published: December 2010

Let Γ be a rank-one arithmetic subgroup of a semisimple Lie group G. For fixed K-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of G, whose discrete part encodes the dimensions of the spaces of square-integrable Γ-automorphic forms. It is shown that this distribution converges to the Plancherel measure of G when Γ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices Γ follows from results of DeGeorge-Wallach and Delorme.
Extreme Pick-Nevanlinna Interpolants
Authors: Fisher Stephen D. , Khavinson Dmitry
Published: December 2010

Following the investigations of B. Abrahamse [1], F. Forelli [11], M. Heins [14] and others, we continue the study of the Pick-Nevanlinna interpolation problem inmultiply-connected planar domains. One major focus is on the problem of characterizing the extreme points of the convex set of interpolants of a fixed data set. Several other related problems are discussed.
Linear Groups Generated by Reflection Tori
Authors: Cohen A. M. , Cuypers H. , Sterk H.
Published: December 2010

A reflection is an invertible linear transformation of a vector space fixing a given hyperplane, its axis, vectorwise and a given complement to this hyperplane, its center, setwise. A reflection torus is a one-dimensional group generated by all reflections with fixed axis and center.

In this paper we classify subgroups of general linear groups (in arbitrary dimension and defined over arbitrary fields) generated by reflection tori.
Symmetric Tessellations on Euclidean Space-Forms
Authors: Hartley Michael I. , McMullen Peter , Schulte Egon
Published: December 2010

It is shown here that, for n ⩾ 2, the n-torus is the only n-dimensional compact euclidean space-form which can admit a regular or chiral tessellation. Further, such a tessellation can only be chiral if n = 2.
Similarity Submodules and Root Systems in Four Dimensions
Authors: Baake Michael , Moody Robert V.
Published: December 2010

Lattices and -modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images according to their indices for certain 4D examples that are related to 4D root systems, both crystallographic and non-crystallographic. We encapsulate their statistics in terms of Dirichlet series generating functions and derive some of their asymptotic properties.
Isomorphism Invariants for Projective Configurations
Authors: Shephard G. C.
Published: December 2010

An isomorphism invariant is an expression, defined for a configuration in the projective plane, which takes the same value for all isomorphic configurations. Examples are given as well as a general method (Nehring sequences) for constructing such invariants.
On the Existence of Similar Sublattices
Authors: Conway J. H. , Rains E. M. , Sloane N. J. A.
Published: December 2010

Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λʹ of index N that is geometrically similar to Λ? When is the sublattice “clean”, in the sense that the boundaries of the Voronoi cells for Λʹ do not intersect Λ?
On Small Complete Sets of Functions
Authors: Aizenberg Lev , Vidras Alekos
Published: December 2010

Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip Tα ⊂ C2. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in Cn.
An Algorithm for Fat Points on P2
Authors: Harbourne Brian
Published: December 2010

Let F be a divisor on the blow-up X of P2 at r general points p1, . . . , pr and let L be the total transform of a line on P2. An approach is presented for reducing the computation of the dimension of the cokernel of the natural map to the case that F is ample. As an application, a formula for the dimension of the cokernel of μF is obtained when r = 7, completely solving the problem of determining the modules in minimal free resolutions of fat point subschemes m1p1 + · · · + m7p7 ⊂ P2. All results hold for an arbitrary algebraically closed ground field k.
Cubic Base Change for GL(2)
Authors: Mao Zhengyu , Rallis Stephen
Published: December 2010

We prove a relative trace formula that establishes the cubic base change for GL(2). One also gets a classification of the image of base change. The case when the field extension is nonnormal gives an example where a trace formula is used to prove lifting which is not endoscopic.
Floer Homology for Knots and SU(2)-Representations for Knot Complements and Cyclic Branched Covers
Authors: Collin Olivier
Published: December 2010

In this article, using 3-orbifolds singular along a knot with underlying space a homology sphere Y3, the question of existence of non-trivial and non-abelian SU(2)-representations of the fundamental group of cyclic branched covers of Y3 along a knot is studied. We first use Floer Homology for knots to derive an existence result of non-abelian SU(2)-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian SU(2)-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in S3.
Hardy Space Estimate for the Product of Singular Integrals
Authors: Miyachi Akihiko
Published: December 2010

Hp estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.
On Some q-Analogs of a Theorem of Kostant-Rallis
Authors: Wallach N. R. , Willenbring J.
Published: December 2010

In the first part of this paper generalizationsof Hesselink’s q-analog of Kostant’smultiplicity formula for the action of a semisimple Lie group on the polynomials on its Lie algebra are given in the context of the Kostant-Rallis theorem. They correspond to the cases of real semisimple Lie groups with one conjugacy class of Cartan subgroup. In the second part of the paper a q-analog of the Kostant-Rallis theorem is given for the real group SL(4, ) (that is SO(4) acting on symmetric 4 × 4 matrices). This example plays two roles. First it contrasts with the examples of the first part. Second it has implications to the study of entanglement of mixed 2 qubit states in quantum computation.
Two-Weight Estimates For Singular Integrals Defined On Spaces Of Homogeneous Type
Authors: Edmunds D. E. , Kokilashvili V. , Meskhi A.
Published: December 2010

Two-weight inequalities of strong and weak type are obtained in the context of spaces of homogeneous type. Various applications are given, in particular to Cauchy singular integrals on regular curves.
On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
Authors: Gui Changfeng , Wei Juncheng
Published: December 2010

We consider the problem

where Ω is a bounded smooth domain in RN, ε > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses multiple boundary spike solutions that concentrate, as ε approaches zero, at multiple critical points of the mean curvature function H(P), P ∈ ∂Ω. It is also proved that this equation has multiple interior spike solutions which concentrate, as ε → 0, at sphere packing points in Ω.

In this paper, we prove the existence of solutions with multiple spikes both on the boundary and in the interior. The main difficulty lies in the fact that the boundary spikes and the interior spikes usually have different scales of error estimation. We have to choose a special set of boundary spikes to match the scale of the interior spikes in a variational approach.
Small Solutions of ϕ1x12 + . . . + ϕnxn2 = 0
Authors: Ou Zhiming M. , Williams Kenneth S.
Published: December 2010

Let ϕ1, . . . , ϕn (n ≥ 2) be nonzero integers such that the equation

is solvable in integers x1, . . . , xn not all zero. It is shown that there exists a solution satisfying

and that the constant 2 is best possible.
Operator Estimates for Fredholm Modules
Authors: Sukochev F. A.
Published: December 2010

We study estimates of the type

where φ(t) = t(1 + t2)−1/2, D0 = D0* is an unbounded linear operator affiliated with a semifinite von Neumann algebra , D − D0 is a bounded self-adjoint linear operator from and , where E(, τ) is a symmetric operator space associated with . In particular, we prove that φ(D) − φ(D0) belongs to the non-commutative Lp-space for some p ∈ (1,∞), provided belongs to the noncommutative weak Lr-space for some r ∈ [1, p). In the case and 1 ≤ p ≤ 2, we show that this result continues to hold under the weaker assumption . This may be regarded as an odd counterpart of A. Connes’ result for the case of even Fredholm modules.
Compact Groups of Operators on Subproportional Quotients of l1m
Authors: Mankiewicz Piotr
Published: December 2010

It is proved that a “typical” n-dimensional quotient Xn of l1m with n = mσ, 0 < σ < 1, has the property

Average

for every compact group G of operators acting on Xn, where dG(T) stands for the normalizedHaar measure on G and the average is taken over all extreme points of the unit ball of Xn. Several consequences of this estimate are presented.
Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties
Authors: Reichstein Zinovy , Youssin Boris
Published: December 2010

Let G be an algebraic group and let X be a generically free G-variety. We show that X can be transformed, by a sequence of blowups with smooth G-equivariant centers, into a G-variety Xʹ with the following property: the stabilizer of every point of Xʹ is isomorphic to a semidirect product U × A of a unipotent group U and a diagonalizable group A.

As an application of this result, we prove new lower bounds on essential dimensions of some algebraic groups. We also show that certain polynomials in one variable cannot be simplified by a Tschirnhaus transformation.
Discrete Series of Classical Groups
Authors: Zhang Yuanli
Published: December 2010

LetGnbe the split classical groups Sp(2n), SO(2n+ 1) and SO(2n) defined over ap-adic field F or the quasi-split classical groupsU(n, n) andU(n+ 1,n) with respect to a quadratic extensionE/F. We prove the self-duality of unitary supercuspidal data of standard Levi subgroups ofGn(F) which give discrete series representations ofGn(F).
Nest Representations of TAF Algebras
Authors: Hopenwasser Alan , Peters Justin R. , Power Stephen C.
Published: December 2010

A nest representation of a strongly maximal TAF algebra A with diagonal D is a representation π for which Lat π(A) is totally ordered. We prove that ker π is a meet irreducible ideal if the spectrum of A is totally ordered or if (after an appropriate similarity) the von Neumann algebra π(D)ʺ contains an atom.
On the Homology of GLnand Higher Pre-Bloch Groups
Authors: Yagunov Serge
Published: December 2010

For every integern> 1 and infinite fieldFwe construct a spectral sequence converging to the homology of GLn(F) relative to the group of monomial matrices GMn(F). Some entries inE2-terms of these spectral sequences may be interpreted as a natural generalization of the Bloch group to higher dimensions. These groups may be characterized as homology of GLnrelatively to GLn-1and GMn. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.
Merit Factors of Polynomials Formed by Jacobi Symbols
Authors: Borwein Peter , Choi Kwok-Kwong Stephen
Published: December 2010

We give explicit formulas for the L4 norm (or equivalently for the merit factors) of various sequences of polynomials related to the polynomials

and

where is the Jacobi symbol.

Two cases of particular interest are when N = pq is a product of two primes and p = q + 2 or p = q + 4. This extends work of Høholdt, Jensen and Jensen and of the authors.

This study arises from a number of conjectures of Erdȍs, Littlewood and others that concern the norms of polynomials with −1, 1 coefficients on the disc. The current best examples are of the above form when N is prime and it is natural to see what happens for composite N.
On the Steinberg Map and Steinberg Cross-Section for a Symmetrizable Indefinite Kac-Moody Group
Authors: Mokler Claus
Published: December 2010

Let G be a symmetrizable indefinite Kac-Moody group over . Let be the characters of the fundamental irreducible representations of G, defined as convergent series on a certain part Gtr-alg ⊆ G. Following Steinberg in the classical case and Brüchert in the affine case, we define the Steinberg map as well as the Steinberg cross section C, together with a natural parametrisation . We investigate the local behaviour of χ on C near , and we show that there exists a neighborhood of (0, . . . , 0) × (1, . . . , 1), on which χ ◦ ω is a regular analytical map, satisfying a certain functional identity. This identity has its origin in an action of the center of G on C.
R-Diagonal Elements and Freeness With Amalgamation
Authors: Nica Alexandru , Shlyakhtenko Dimitri , Speicher Roland
Published: December 2010

The concept of R-diagonal element was introduced in [5], and was subsequently found to have applications to several problems in free probability. In this paper we describe a new approach to R-diagonality, which relies on freeness with amalgamation. The class of R-diagonal elements is enlarged to contain examples living in non-tracial *-probability spaces, such as the generalized circular elements of [7].
Values of the Dedekind Eta Function at Quadratic Irrationalities: Corrigendum
Authors: van der Poorten Alfred J. , Williams Kenneth S.
Published: December 2010

Habib Muzaffar of Carleton University has pointed out to the authors that in their paper [A] only the result

follows from the prime ideal theorem with remainder for ideal classes, and not the stronger result

stated in Lemma 5.2. This necessitates changes in Sections 5 and 6 of [A]. The main results of the paper are not affected by these changes. It should also be noted that, starting on page 177 of [A], each and every occurrence of o(s − 1) should be replaced by o(1).

Sections 5 and 6 of [A] have been rewritten to incorporate the abovementioned correction and are given below. They should replace the original Sections 5 and 6 of [A].
Spaces of Lorentz Multipliers
Authors: Hare Kathryn E. , Sato Enji
Published: December 2010

We study when the spaces of Lorentz multipliers from Lp,t → Lp,s are distinct. Our main interest is the case when s < t, the Lorentz-improving multipliers. We prove, for example, that the space of multipliers which map Lp,t → Lp,s is different from those mapping Lp,t → Lp,s if either r = p or p′ and 1/s − 1/t ≠ 1/u − 1/v, or r ≠ p or p′. These results are obtained by making careful estimates of the Lorentz multiplier norms of certain linear combinations of Fejer or Dirichlet kernels. For the case when the first indices are different the linear combination we analyze is in the spirit of a Rudin-Shapiro polynomial.
Avoiding Patterns in the Abelian Sense
Authors: Currie J. , Linek V.
Published: December 2010

We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some properties of ω-words avoiding these patterns.
Differential Structure of Orbit Spaces
Authors: Cushman Richard , Śniatycki Jędrzej
Published: December 2010

We present a new approach to singular reduction of Hamiltonian systems with symmetries. The tools we use are the category of differential spaces of Sikorski and the Stefan-Sussmann theorem. The former is applied to analyze the differential structure of the spaces involved and the latter is used to prove that some of these spaces are smooth manifolds.

Our main result is the identification of accessible sets of the generalized distribution spanned by the Hamiltonian vector fields of invariant functions with singular reduced spaces. We are also able to describe the differential structure of a singular reduced space corresponding to a coadjoint orbit which need not be locally closed.
AsymptoticK-Theory for Groups Acting onÃ2Buildings
Authors: Robertson Guyan , Steger Tim
Published: December 2010

Let Γ be a torsion free lattice inG= PGL(3,) whereis a nonarchimedean local field. Then Γ acts freely on the affine Bruhat-Tits building ℬ ofGand there is an induced action on the boundary Ω of ℬ. The crossed productC*-algebra(Γ) =C(Ω) ⋊ Γ depends only on Γ and is classified by itsK-theory. This article shows how to compute theK-theory of(Γ) and of the larger class of rank two Cuntz-Krieger algebras.
Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values ofL-Functions ats= 1, and Explicit Lower Bounds for Relative Class Numbers of CM-Fields
Authors: Louboutin Stéphane
Published: December 2010

We provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at$s=1$of$L$-series associated with primitive characters on ray class groups of number fields. To make it quite clear to the reader how useful such bounds are when dealing with class number problems for CM-fields, we deduce an upper bound for the root discriminants of the normal CM-fields with (relative) class number one.
Quasi-Poisson Manifolds
Authors: Alekseev A. , Kosmann-Schwarzbach Y. , Meinrenken E.
Published: December 2010

A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.
Parametric Representation of Univalent Mappings in Several Complex Variables
Authors: Graham Ian , Hamada Hidetaka , Kohr Gabriela
Published: December 2010

Let B be the unit ball of with respect to an arbitrary norm. We prove that the analog of the Carathéodory set, i.e. the set of normalized holomorphic mappings from B into of “positive real part”, is compact. This leads to improvements in the existence theorems for the Loewner differential equation in several complex variables. We investigate a subset of the normalized biholomorphic mappings of B which arises in the study of the Loewner equation, namely the set S0(B) of mappings which have parametric representation. For the case of the unit polydisc these mappings were studied by Poreda, and on the Euclidean unit ball they were studied by Kohr. As in Kohr’s work, we consider subsets of S0(B) obtained by placing restrictions on the mapping from the Carathéodory set which occurs in the Loewner equation. We obtain growth and covering theorems for these subsets of S0(B) as well as coefficient estimates, and consider various examples. Also we shall see that in higher dimensions there exist mappings in S(B) which can be imbedded in Loewner chains, but which do not have parametric representation.
On Connected Components of Shimura Varieties
Authors: Haines Thomas J.
Published: December 2010

We study the cohomology of connected components of Shimura varieties coming from the group GSp2g, by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character ϖ on the group of connected components of we define an operator L(ω) on the cohomology groups with compact supports Hic(, ), and then we prove that the virtual trace of the composition of L(ω) with a Hecke operator f away from p and a sufficiently high power of a geometric Frobenius , can be expressed as a sum of ω-weighted (twisted) orbital integrals (where ω-weighted means that the orbital integrals and twisted orbital integrals occuring here each have a weighting factor coming from the character ϖ). As the crucial step, we define and study a new invariant α1(γ0; γ, δ) which is a refinement of the invariant α(γ0; γ, δ) defined by Kottwitz. This is done by using a theorem of Reimann and Zink.
Rational Solutions of Painlevé Equations
Authors: Wenjun Yuan , Yezhou Li
Published: December 2010

Consider the sixth Painlevé equation (P6) below where α, β, γ and δ are complex parameters. We prove the necessary and sufficient conditions for the existence of rational solutions of equation (P6) in term of special relations among the parameters. The number of distinct rational solutions in each case is exactly one or two or infinite. And each of them may be generated by means of transformation group found by Okamoto [7] and Bäcklund transformations found by Fokas and Yortsos [4]. A list of rational solutions is included in the appendix. For the sake of completeness, we collected all the corresponding results of other five Painlevé equations (P1)−(P5) below, which have been investigated by many authors [1]–[7].
Chief Factor Sizes in Finitely Generated Varieties
Authors: Kearnes K. A. , Kiss E. W. , Szendrei Á. , Willard R. D.
Published: December 2010

Let A be a k-element algebra whose chief factor size is c. We show that if B is in the variety generated by A, then any abelian chief factor of B that is not strongly abelian has size at most ck−1. This solves Problem 5 of The Structure of Finite Algebras, by D. Hobby and R. McKenzie. We refine this bound to c in the situation where the variety generated by A omits type 1. As a generalization, we bound the size of multitraces of types 1, 2, and 3 by extending coordinatization theory. Finally, we exhibit some examples of bad behavior, even in varieties satisfying a congruence identity.
Nilpotent Orbits and Whittaker Functions for Derived Functor Modules of Sp(2, ℝ)
Authors: Miyazaki Takuya
Published: December 2010

We study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp(2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in and the asymptotic support of the cohomological representation.
Spherical Functions for the Semisimple Symmetric Pair (Sp(2, ℝ), SL(2, ℂ))
Authors: Moriyama Tomonori
Published: December 2010

Let π be an irreducible generalized principal series representation of G = Sp(2, ℝ) induced from its Jacobi parabolic subgroup. We show that the space of algebraic intertwining operators from π to the representation induced from an irreducible admissible representation of SL(2, ℂ) in G is at most one dimensional. Spherical functions in the title are the images of K-finite vectors by this intertwining operator. We obtain an integral expression of Mellin-Barnes type for the radial part of our spherical function.
Convexité, complète monotonie et inégalités sur les fonctions zèta et gamma, sur les fonctions des opérateurs de Baskakov et sur des fonctions arithmétiques
Authors: Bastien G. , Rogalski M.
Published: December 2010

Nous prouvons un encadrement optimal pour la quantité pour x ≥ 0 et s > 1, qui améliore l'encadrement standard par des int égrales. Cet encadrement entraîne des inégalités sur la fonction ζ de Riemann, et amène à conjecturer la monotonie de la fonction . On donne des applications à l'étude de la convexité de fonctions liées à la fonction Γ d'Euler et à la majoration optimale des fonctions élémentaires intervenant dans les opérateurs de Baskakov. Puis, nous étendons aux fonctions complètement monotones sur ]0, +∞[ les résultats établis pour la fonction , et nous en déduisons des preuves élémentaires du comportement, quand z tend vers 1, des séries génératrices de certaines fonctions arithmétiques. Enfin, nous prouvons qu'une partie du résultat se généralise à une classe de fonctions convexes positives décroissantes.
Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications
Authors: Boivin André , Gauthier Paul M. , Paramonov Petr V.
Published: December 2010

Given a homogeneous elliptic partial differential operator L with constant complex coefficients and a class of functions (jet-distributions) which are defined on a (relatively) closed subset of a domain Ω in Rn and which belong locally to a Banach space V, we consider the problem of approximating in the norm of V the functions in this class by “analytic” and “meromorphic” solutions of the equation Lu = 0. We establish new Roth, Arakelyan (including tangential) and Carleman type theorems for a large class of Banach spaces V and operators L. Important applications to boundary value problems of solutions of homogeneous elliptic partial differential equations are obtained, including the solution of a generalized Dirichlet problem.
Bifurcations of Limit Cycles From Infinity in Quadratic Systems
Authors: Gavrilov Lubomir , Iliev Iliya D.
Published: December 2010

We investigate the bifurcation of limit cycles in one-parameter unfoldings of quadractic differential systems in the plane having a degenerate critical point at infinity. It is shown that there are three types of quadratic systems possessing an elliptic critical point which bifurcates from infinity together with eventual limit cycles around it. We establish that these limit cycles can be studied by performing a degenerate transformation which brings the system to a small perturbation of certain well-known reversible systems having a center. The corresponding displacement function is then expanded in a Puiseux series with respect to the small parameter and its coefficients are expressed in terms of Abelian integrals. Finally, we investigate in more detail four of the cases, among them the elliptic case (Bogdanov-Takens system) and the isochronous center S3. We show that in each of these cases the corresponding vector space of bifurcation functions has the Chebishev property: the number of the zeros of each function is less than the dimension of the vector space. To prove this we construct the bifurcation diagram of zeros of certain Abelian integrals in a complex domain.