bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Characterization of two Weight Norm Inequalities for One-Sided Operators of Fractional Type
Authors: Lorente Maria 
Published: December 2010

AbstractIn this paper we give a characterization of the pairs of weights (ω, v) such that T maps Lp(v) into Lq(ω),where T is a general one-sided operator that includes as a particular case theWeyl fractional integral. As an applicationwe solve the following problem: given a weight v, when is there a nontrivial weight ω such that T maps Lp(v) into Lq(ω)?
Asymptotic Shape of Finite Packings
Authors: Böröczky KáRoly , Schnell Uwe 
Published: December 2010

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

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

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

AbstractWe study the intertwining operator and h-harmonics in Dunkl's theory on h–harmonics associated with reflection groups. Based on a biorthogonality between the ordinary harmonics and the action of the intertwining operator V on the harmonics, the main result provides a method to compute the action of the intertwining operator V on polynomials and to construct an orthonormal basis for the space of h-harmonics.
Asymptotic Transformations of q-Series
Authors: McIntosh Richard J. 
Published: December 2010

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

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

AbstractThis paper deals with periodic solutions for the billiard problem in a bounded open set of ℝN which are limits of regular solutions of Lagrangian systems with a potential well. We give a precise link between the Morse index of approximate solutions (regarded as critical points of Lagrangian functionals) and the properties of the bounce trajectory to which they converge.
The Homology of Singular Polygon Spaces
Authors: Kamiyama Yasuhiko 
Published: December 2010

AbstractLet Mn be the variety of spatial polygons P = (a1, a2, … ,an) whose sides are vectors ai ∈ R3 of length |ai| = 1 (1 ≤ i ≤ n), up to motion in R3. It is known that for odd n, Mn is a smooth manifold, while for even n, Mn has cone-like singular points. For odd n, the rational homology of Mn was determined by Kirwan and Klyachko [6], [9]. The purpose of this paper is to determine the rational homology of Mn for even n. For even n, let be the manifold obtained from Mn by the resolution of the singularities. Then we also determine the integral homology of .
Indecomposable Almost Free Modules—The Local Case
Authors: Göbel Rüdiger , Shelah Saharon 
Published: December 2010

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

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

AbstractLet π:X → S be a finite type morphism of noetherian schemes. A smooth formal embedding of X (over S) is a bijective closed immersion X ⊂ 𝖃 , where 𝖃 is a noetherian formal scheme, formally smooth over S. An example of such an embedding is the formal completion 𝖃 = Y/X where X ⊂ Y is an algebraic embedding. Smooth formal embeddings can be used to calculate algebraic De Rham(co)homology.Our main application is an explicit construction of the Grothendieck residue complex when S is a regular scheme. By definition the residue complex is the Cousin complex of π!OS, as in [RD]. We start with I-C. Huang's theory of pseudofunctors on modules with 0-dimensional support, which provides a graded sheaf .We then use smooth formal embeddings to obtain the coboundary operator . We exhibit a canonical isomorphism between the complex (K·x/s, δ ) and the residue complex of [RD]. When π is equidimensional of dimension n and generically smooth we show that H-nK·x/s is canonically isomorphic to to the sheaf of regular differentials of Kunz-Waldi [KW].Another issue we discuss is Grothendieck Duality on a noetherian formal scheme 1d583 . Our results on duality are used in the construction of K·x/s.
Partial Characters and Signed Quotient Hypergroups
Authors: Rösler Margit , Voit Michael 
Published: December 2010

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

AbstractWe construct meromorphic functions with asymptotic power series expansion in z−1 at ∞ on an Arakelyan set A having prescribed zeros and poles outside A. We use our results to prove approximation theorems where the approximating function fulfills interpolation restrictions outside the set of approximation.
Spectral Estimates for Towers of Noncompact Quotients
Authors: Deitmar Anton , Hoffman Werner 
Published: December 2010

AbstractWe prove a uniform upper estimate on the number of cuspidal eigenvalues of the Γ-automorphic Laplacian below a given bound when Γ varies in a family of congruence subgroups of a given reductive linear algebraic group. Each Γ in the family is assumed to contain a principal congruence subgroup whose index in Γ does not exceed a fixed number. The bound we prove depends linearly on the covolume of Γ and is deduced from the analogous result about the cut-off Laplacian. The proof generalizes the heat-kernel method which has been applied by Donnelly in the case of a fixed lattice Γ.
A Homotopy of Quiver Morphisms with Applications to Representations
Authors: Enochs Edgar E. , Herzog Ivo 
Published: December 2010

AbstractIt is shown that a morphism of quivers having a certain path lifting property has a decomposition that mimics the decomposition of maps of topological spaces into homotopy equivalences composed with fibrations. Such a decomposition enables one to describe the right adjoint of the restriction of the representation functor along a morphism of quivers having this path lifting property. These right adjoint functors are used to construct injective representations of quivers. As an application, the injective representations of the cyclic quivers are classified when the base ring is left noetherian. In particular, the indecomposable injective representations are described in terms of the injective indecomposable R-modules and the injective indecomposable R[x; x−1]-modules.
Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations
Authors: Bshouty D. , Hengartner W. 
Published: December 2010

AbstractIn this article we characterize the univalent harmonic mappings from the exterior of the unit disk, Δ, onto a simply connected domain Ω containing infinity and which are solutions of the system of elliptic partial differential equations where the second dilatation function a(z) is a finite Blaschke product. At the end of this article, we apply our results to nonparametric minimal surfaces having the property that the image of its Gauss map is the upper half-sphere covered once or twice.
Smooth Finite Dimensional Embeddings
Authors: Mansfield R. , Movahedi-Lankarani H. , Wells R. 
Published: December 2010

AbstractWe give necessary and sufficient conditions for a norm-compact subset of a Hilbert space to admit aC1embedding into a finite dimensional Euclidean space. Using quasibundles, we prove a structure theorem saying that the stratum ofn-dimensional points is contained in ann-dimensionalC1submanifold of the ambient Hilbert space. This work sharpens and extends earlier results of G. Glaeser on paratingents. As byproducts we obtain smoothing theorems for compact subsets of Hilbert space and disjunction theorems for locally compact subsets of Euclidean space.
On Functions Satisfying Modular Equations for Infinitely Many Primes
Authors: Kozlov Dmitry N. 
Published: December 2010

AbstractIn this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are:1)every such function is analytic in the upper half plane;2)if such function takes the same value in two different pointsz1andz2then there exists anf-preserving analytic bijection between neighbourhoods ofz1andz2.
The Homology of Abelian Covers of Knotted Graphs
Authors: Litherland R. A. 
Published: December 2010

AbstractLet be a regular branched cover of a homology 3-sphere M with deck group and branch set a trivalent graph Γ; such a cover is determined by a coloring of the edges of Γ with elements of G. For each index-2 subgroup H of G, MH = /H is a double branched cover of M. Sakuma has proved that H1() is isomorphic, modulo 2-torsion, to ⊕HH1(MH), and has shown that H1() is determined up to isomorphism by ⊕HH1(MH) in certain cases; specifically, when d = 2 and the coloring is such that the branch set of each cover MH → M is connected, and when d = 3 and Γ is the complete graph K4. We prove this for a larger class of coverings: when d = 2, for any coloring of a connected graph; when d = 3 or 4, for an infinite class of colored graphs; and when d = 5, for a single coloring of the Petersen graph.
Endoscopic L-Functions and a Combinatorial Identity
Authors: Arthur James 
Published: December 2010

AbstractThe trace formula contains terms on the spectral side that are constructed from unramified automorphic L-functions. We shall establish an identify that relates these terms with corresponding terms attached to endoscopic groups of G. In the process, we shall show that the L-functions of G that come from automorphic representations of endoscopic groups have meromorphic continuation.
Reflection Subquotients of Unitary Reflection Groups
Authors: Lehrer G. I. , Springer T. A. 
Published: December 2010

AbstractLet G be a finite group generated by (pseudo-) reflections in a complex vector space and let g be any linear transformation which normalises G. In an earlier paper, the authors showed how to associate with any maximal eigenspace of an element of the coset gG, a subquotient of G which acts as a reflection group on the eigenspace. In this work, we address the questions of irreducibility and the coexponents of this subquotient, as well as centralisers in G of certain elements of the coset. A criterion is also given in terms of the invariant degrees of G for an integer to be regular for G. A key tool is the investigation of extensions of invariant vector fields on the eigenspace, which leads to some results and questions concerning the geometry of intersections of invariant hypersurfaces.
Numerical Ranges Arising from Simple Lie Algebras
Authors: Li Chi-Kwong , Tam Tin-Yau 
Published: December 2010

AbstractA unified formulation is given to various generalizations of the classical numerical range including the c-numerical range, congruence numerical range, q-numerical range and von Neumann range. Attention is given to those cases having connections with classical simple real Lie algebras. Convexity and inclusion relation involving those generalized numerical ranges are investigated. The underlying geometry is emphasized.
On Orbit Closures of Symmetric Subgroups in Flag Varieties
Authors: Brion Michel , Helminck Aloysius G. 
Published: December 2010

AbstractWe study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K \ G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic subgroups. We also describe the decomposition of any (K, P)-double coset in G into (K, B)-double cosets, where B ⊆ P is a Borel subgroup. Finally, for certain K-orbit closures X ⊆ G/B, and for any homogeneous line bundle on G/B having nonzero global sections, we show that the restriction map resX : H0(G/B, ) → H0(X, ) is surjective and that Hi(X, ) = 0 for i ≥ 1. Moreover, we describe the K-module H0(X, ). This gives information on the restriction to K of the simple G-module H0(G/B, ). Our construction is a geometric analogue of Vogan and Sepanski’s approach to extremal K-types.
Singularités quasi-ordinaires toriques et polyèdre de Newton du discriminant
Authors: González Pérez P. D. 
Published: December 2010

AbstractNous étudions les polynômes à coefficients dans l’anneau de germes de fonctions holomorphes au point spécial d’une variété torique affine. Nous généralisons à ce cas la paramétrisation classique des singularités quasi-ordinaires. Cela fait intervenir d’une part une généralization de l’algorithme de Newton-Puiseux, et d’autre part une relation entre le polyèdre de Newton du discriminant de F par rapport à Y et celui de F au moyen du polytope-fibre de Billera et Sturmfels [3]. Cela nous permet enfin de calculer, sous des hypothèses de non dégénérescence, les sommets du polyèdre de Newton du discriminant a partir de celui de F, et les coefficients correspondants à partir des coefficients des exposants de F qui sont dans les arˆetes de son polyèdre de Newton.
Correspondences, von Neumann Algebras and Holomorphic L2 Torsion
Authors: Carey A. , Farber M. , Mathai V. 
Published: December 2010

AbstractGiven a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic L2 torsion, which lies in the determinant line of the twisted L2 Dolbeault cohomology and represents a volume element there. Here we utilise the theory of determinant lines of Hilbertian modules over finite von Neumann algebras as developed in [CFM]. This specialises to the Ray-Singer-Quillen holomorphic torsion in the finite dimensional case. We compute ametric variation formula for the holomorphic L2 torsion, which shows that it is not in general independent of the choice of Hermitian metrics on the complex manifold and on the holomorphic Hilbertian bundle, which are needed to define it. We therefore initiate the theory of correspondences of determinant lines, that enables us to define a relative holomorphic L2 torsion for a pair of flat Hilbertian bundles, which we prove is independent of the choice of Hermitian metrics on the complex manifold and on the flat Hilbertian bundles.
The Distributions in the Invariant Trace Formula Are Supported on Characters
Authors: Kottwitz Robert E. , Rogawski Jonathan D. 
Published: December 2010

AbstractJ. Arthur put the trace formula in invariant form for all connected reductive groups and certain disconnected ones. However his work was written so as to apply to the general disconnected case, modulo two missing ingredients. This paper supplies one of those missing ingredients, namely an argument in Galois cohomology of a kind first used by D. Kazhdan in the connected case.
W-Groups under Quadratic Extensions of Fields
Authors: Mináč Ján , Smith Tara L. 
Published: December 2010

AbstractTo each field F of characteristic not 2, one can associate a certain Galois group , the so-called W-group of F, which carries essentially the same information as the Witt ring W(F) of F. In this paperwe investigate the connection between and (√a), where F(√a) is a proper quadratic extension of F. We obtain a precise description in the case when F is a pythagorean formally real field and a = −1, and show that the W-group of a proper field extension K/F is a subgroup of the W-group of F if and only if F is a formally real pythagorean field and K = F(√−1). This theorem can be viewed as an analogue of the classical Artin-Schreier’s theorem describing fields fixed by finite subgroups of absolute Galois groups. We also obtain precise results in the case when a is a double-rigid element in F. Some of these results carry over to the general setting.
Real Interpolation with Logarithmic Functors and Reiteration
Authors: Evans W. D. , Opic B. 
Published: December 2010

AbstractWe present “reiteration theorems” with limiting values θ = 0 and θ = 1 for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].
Canonical Resolution of a Quasi-ordinary Surface Singularity
Authors: Ban Chunsheng , McEwan Lee J. 
Published: December 2010

AbstractWe describe the embedded resolution of an irreducible quasi-ordinary surface singularity (V, p) which results from applying the canonical resolution of Bierstone-Milman to (V, p). We show that this process depends solely on the characteristic pairs of (V, p), as predicted by Lipman. We describe the process explicitly enough that a resolution graph for f could in principle be obtained by computer using only the characteristic pairs.
Orbital Integrals on p-Adic Lie Algebras
Authors: Herb Rebecca A. 
Published: December 2010

AbstractLet G be a connected reductive p-adic group and let be its Lie algebra. Let be any G-orbit in . Then the orbital integral corresponding to is an invariant distribution on , and Harish-Chandra proved that its Fourier transform is a locally constant function on the set of regular semisimple elements of . If is a Cartan subalgebra of , and ω is a compact subset of ∩ , we give a formula for (tH) for H ε ω and t ε F× sufficiently large. In the case that is a regular semisimple orbit, the formula is already known by work of Waldspurger. In the case that is a nilpotent orbit, the behavior of at infinity is already known because of its homogeneity properties. The general case combines aspects of these two extreme cases. The formula for at infinity can be used to formulate a “theory of the constant term” for the space of distributions spanned by the Fourier transforms of orbital integrals. It can also be used to show that the Fourier transforms of orbital integrals are “linearly independent at infinity.”
Stratification Theory from the Weighted Point of View
Authors: Fukui Toshizumi , Paunescu Laurentiu 
Published: December 2010

AbstractIn this paper, we investigate stratification theory in terms of the defining equations of strata and maps (without tube systems), offering a concrete approach to show that some given family is topologically trivial. In this approach, we consider a weighted version of (w)-regularity condition and Kuo’s ratio test condition.