bluuebunny/crossref_metadata_2025_split huggingface dataset:
Generalized Factorization in Hardy Spaces and the Commutant of Toeplitz Operators
Authors: Stessin Michael , Zhu Kehe 
Published: December 2010

AbstractEvery classical inner function φ in the unit disk gives rise to a certain factorization of functions in Hardy spaces. This factorization, which we call the generalized Riesz factorization, coincides with the classical Riesz factorization when φ(z) = z. In this paper we prove several results about the generalized Riesz factorization, and we apply this factorization theory to obtain a new description of the commutant of analytic Toeplitz operators with inner symbols on a Hardy space. We also discuss several related issues in the context of the Bergman space.
Certain Operators with Rough Singular Kernels
Authors: Chen Jiecheng , Fan Dashan , Ying Yiming 
Published: December 2010

AbstractWe study the singular integral operatordefined on all test functions f, where b is a bounded function, α ≥ 0, Ω (yʻ) is an integrable function on the unit sphere Sn-1 satisfying certain cancellation conditions. We prove that, for 1 < p < ∞, TΩ,α extends to a bounded operator from the Sobolev space to the Lebesgue space Lp with Ω being a distribution in the Hardy space Hq(Sn-1) where . The result extends some known results on the singular integral operators. As applications, we obtain the boundedness for TΩ,α on the Hardy spaces, as well as the boundedness for the truncated maximal operator .
Sturm-Liouville Problems Whose Leading Coefficient Function Changes Sign
Authors: Cao Xifang , Kong Qingkai , Wu Hongyou , Zettl Anton 
Published: December 2010

AbstractFor a given Sturm-Liouville equation whose leading coefficient function changes sign, we establish inequalities among the eigenvalues for any coupled self-adjoint boundary condition and those for two corresponding separated self-adjoint boundary conditions. By a recent result of Binding and Volkmer, the eigenvalues (unbounded from both below and above) for a separated self-adjoint boundary condition can be numbered in terms of the Prüfer angle; and our inequalities can then be used to index the eigenvalues for any coupled self-adjoint boundary condition. Under this indexing scheme, we determine the discontinuities of each eigenvalue as a function on the space of such Sturm-Liouville problems, and its range as a function on the space of self-adjoint boundary conditions. We also relate this indexing scheme to the number of zeros of eigenfunctions. In addition, we characterize the discontinuities of each eigenvalue under a different indexing scheme.
Lie Groups of Measurable Mappings
Authors: Glöckner Helge 
Published: December 2010

AbstractWe describe new construction principles for infinite-dimensional Lie groups. In particular, given any measure space (X; Σ, μ) and (possibly infinite-dimensional) Lie group G, we construct a Lie group L∞(X; G), which is a Fréchet-Lie group if G is so. We also show that the weak direct product of an arbitrary family (Gi)i∈I of Lie groups can be made a Lie group, modelled on the locally convex direct sum .
Norms of Complex Harmonic Projection Operators
Authors: Casarino Valentina 
Published: December 2010

AbstractIn this paper we estimate the (Lp – L2)-norm of the complex harmonic projectors πℓ,ℓ′, 1 ≤ p ≤ 2, uniformly with respect to the indexes ℓ, ℓ′. We provide sharp estimates both for the projectors πℓ,ℓ′, when ℓ, ℓ′ belong to a proper angular sector in ℕ × ℕ, and for the projectors πℓ0 and π0ℓ. The proof is based on an extension of a complex interpolation argument by C. Sogge. In the appendix, we prove in a direct way the uniform boundedness of a particular zonal kernel in the L1 norm on the unit sphere of ℝ2n.
The Ideal Structures of Crossed Products of Cuntz Algebras by Quasi-Free Actions of Abelian Groups
Authors: Katsura Takeshi 
Published: December 2010

AbstractWe completely determine the ideal structures of the crossed products of Cuntz algebras by quasi-free actions of abelian groups and give another proof of A. Kishimoto's result on the simplicity of such crossed products. We also give a necessary and sufficient condition that our algebras become primitive, and compute the Connes spectra andK-groups of our algebras.
Euclidean Rings of Algebraic Integers
Authors: Harper Malcolm , Murty M. Ram 
Published: December 2010

AbstractLet K be a finite Galois extension of the field of rational numbers with unit rank greater than 3. We prove that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann hypothesis for Dedekind zeta functions. We now prove this unconditionally.
High-Dimensional Graphical Networks of Self-Avoiding Walks
Authors: Holmes Mark , Járai Antal A. , Sakai Akira , Slade Gordon 
Published: December 2010

AbstractWe use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour for sufficiently spread-out networks on ℤd in dimensions d > 4.
Estimates of Hausdorff Dimension for the Non-Wandering Set of an Open Planar Billiard
Authors: Kenny Robert 
Published: December 2010

AbstractThe billiard flow in the plane has a simple geometric definition; the movement along straight lines of points except where elastic reflections are made with the boundary of the billiard domain. We consider a class of open billiards, where the billiard domain is unbounded, and the boundary is that of a finite number of strictly convex obstacles. We estimate the Hausdorff dimension of the nonwandering set M0 of the discrete time billiard ball map, which is known to be a Cantor set and the largest invariant set. Under certain conditions on the obstacles, we use a well-known coding ofM0 [Mor91] and estimates using convex fronts related to the derivative of the billiard ball map [Sto03] to estimate the Hausdorff dimension of local unstable sets. Consideration of the local product structure then yields the desired estimates, which provide asymptotic bounds on the Hausdorff dimension's convergence to zero as the obstacles are separated.
Structure of Modules Induced from Simple Modules with Minimal Annihilator
Authors: Khomenko Oleksandr , Mazorchuk Volodymyr 
Published: December 2010

AbstractWe study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to proper standard modules in some parabolic generalization of the Bernstein-Gelfand-Gelfand category and prove that the blocks of this parabolic category are equivalent to certain blocks of the category of Harish-Chandra bimodules. From this we derive, in particular, an irreducibility criterion for generalized Verma modules. We also compute the composition multiplicities of those simple subquotients, which correspond to the induction from simple modules whose annihilators are minimal primitive ideals.
Infinite-Dimensional Polyhedrality
Authors: Fonf Vladimir P. , Veselý Libor 
Published: December 2010

AbstractThis paper deals with generalizations of the notion of a polytope to infinite dimensions. The most general definition is the following: a bounded closed convex subset of a Banach space is called a polytope if each of its finite-dimensional affine sections is a (standard) polytope.We study the relationships between eight known definitions of infinite-dimensional polyhedrality. We provide a complete isometric classification of them, which gives solutions to several open problems. An almost complete isomorphic classification is given as well (only one implication remains open).
Geodesics in a Manifold with Heisenberg Group as Boundary
Authors: Ni Yilong 
Published: December 2010

AbstractThe Heisenberg group is considered as the boundary of a manifold. A class of hypersurfaces in this manifold can be regarded as copies of the Heisenberg group. The properties of geodesics in the interior and on the hypersurfaces are worked out in detail. These properties are strongly related to those of the Heisenberg group.
Differentiability Properties of Optimal Value Functions
Authors: Penot Jean-Paul 
Published: December 2010

AbstractDifferentiability properties of optimal value functions associated with perturbed optimization problems require strong assumptions. We consider such a set of assumptions which does not use compactness hypothesis but which involves a kind of coherence property. Moreover, a strict differentiability property is obtained by using techniques of Ekeland and Lebourg and a result of Preiss. Such a strengthening is required in order to obtain genericity results.
Finding and Excluding b-ary Machin-Type Individual Digit Formulae
Authors: Borwein Jonathan M. , Borwein David , Galway William F. 
Published: December 2010

AbstractConstants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base b) have interesting computational properties, such as allowing single digits in their base b expansion to be independently computed, and there are hints that they should be normal numbers, i.e., that their base b digits are randomly distributed. We study a formally limited subset of BBP formulae, which we call Machin-type BBP formulae, for which it is relatively easy to determine whether or not a given constant κ has a Machin-type BBP formula. In particular, given b ∈ ℕ, b > 2, b not a proper power, a b-ary Machin-type BBP arctangent formula for κ is a formula of the form κ = Σmam arctan(–b–m), am ∈ ℚ, while when b = 2, we also allow terms of the form am arctan(1/(1 – 2m)). Of particular interest, we show that π has no Machin-type BBP arctangent formula when b ≠ 2. To the best of our knowledge, when there is no Machin-type BBP formula for a constant then no BBP formula of any form is known for that constant.
Fubini's Theorem for Ultraproducts of Noncommutative Lp-Spaces
Authors: Junge Marius 
Published: December 2010

AbstractLet (ℳi)i∈I, be families of von Neumann algebras and be ultrafilters in I, J, respectively. Let 1 ≤ p < ∞ and n ∈ ℕ. Let x1,… ,xn in ΠLp(ℓi ) and y1,… ,yn in be bounded families. We show the following equalityFor p = 1 this Fubini type result is related to the local reflexivity of duals of C*-algebras. This fails for p = ∞.
Non-Orientable Surfaces and Dehn Surgeries
Authors: Matignon D. , Sayari N. 
Published: December 2010

AbstractLetKbe a knot inS3. This paper is devoted to Dehn surgeries which create 3-manifolds containing a closed non-orientable surface. We look at the slopep/qof the surgery, the Euler characteristic χ() of the surface and the intersection numbersbetweenand the core of the Dehn surgery. We prove that if χ() ≥ 15 – 3q, thens= 1. Furthermore, ifs= 1 thenq≤ 4 – 3χ() orKis cabled andq≤ 8 – 5χ(). As consequence, ifKis hyperbolic and χ() = –1, thenq≤ 7.
Semi-classical Integrability, Hyperbolic Flows and the Birkhoff Normal Form
Authors: Rouleux Michel 
Published: December 2010

AbstractWe prove that a Hamiltonianp∈C∞(T*Rn) is locally integrable near a non-degenerate critical point ρ0of the energy, provided that the fundamental matrix at ρ0has rationally independent eigenvalues, none purely imaginary. This is done by using Birkhoff normal forms, which turn out to be convergent in theC∞sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transformation. Then we investigate the complex case, showing that whenpis holomorphic near ρ0∈T*Cn, then Repbecomes integrable in the complex domain for real times, while the Birkhoff series and the Birkhoff transforms may not converge,i.e., pmay not be integrable. These normal forms also hold in the semi-classical frame.
Cycle-Level Intersection Theory for Toric Varieties
Authors: Thomas Hugh 
Published: December 2010

AbstractThis paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor with an invariant cycle on a toric variety. For a toric variety defined by a fan inN, the choice consists of giving an inner product or a complete flag forMQ= ℚ ⊗ Hom(N, ℤ), or more generally giving for each cone σ in the fan a linear subspace ofMQcomplementary to σ⊥, satisfying certain compatibility conditions. We show that these intersection cycles have properties analogous to the usual intersections modulo rational equivalence. IfXis simplicial (for instance, ifXis non-singular), we obtain a commutative ring structure to the invariant cycles ofXwith rational coefficients. This ring structure determines cycles representing certain characteristic classes of the toric variety. We also discuss how to define intersection cycles that require no choices, at the expense of increasing the size of the coefficient field.
The Fourier Algebra for Locally Compact Groupoids
Authors: Paterson Alan L. T. 
Published: December 2010

AbstractWe introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.
Equivariant Formality for Actions of Torus Groups
Authors: Scull Laura 
Published: December 2010

AbstractThis paper contains a comparison of several definitions of equivariant formality for actions of torus groups. We develop and prove some relations between the definitions. Focusing on the case of the circle group, we use S1-equivariant minimal models to give a number of examples of S1-spaces illustrating the properties of the various definitions.
Second Order Operators on a Compact Lie Group
Authors: Fegan H. D. , Steer B. 
Published: December 2010

AbstractWe describe the structure of the space of second order elliptic differential operators on a homogenous bundle over a compact Lie group. Subject to a technical condition, these operators are homotopic to the Laplacian. The technical condition is further investigated, with examples givenwhere it holds and others where it does not. Since many spectral invariants are also homotopy invariants, these results provide information about the invariants of these operators.
On a Conjecture of Birch and Swinnerton-Dyer
Authors: Kuo Wentang , Murty M. Ram 
Published: December 2010

AbstractLet E/Q be an elliptic curve defined by the equation For a prime p, defineAs a precursor to their celebrated conjecture, Birch and Swinnerton-Dyer originally conjectured that for some constant c,Let αp and βp be the eigenvalues of the Frobenius at p. Define
Hermitian Yang–Mills–Higgs Metrics on Complete Kähler Manifolds
Authors: Zhang Xi 
Published: December 2010

AbstractIn this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact Kähler manifolds.
Deformations ofG2and Spin(7) Structures
Authors: Karigiannis Spiro 
Published: December 2010

AbstractWe consider some deformations ofG2-structures on 7-manifolds. We discover a canonical way to deform aG2-structure by a vector field in which the associated metric gets “twisted” in some way by the vector cross product. We present a system of partial differential equations for an unknown vector fieldwwhose solution would yield a manifold with holonomyG2. Similarly we consider analogous constructions for Spin(7)-structures on 8-manifolds. Some of the results carry over directly, while others do not because of the increased complexity of the Spin(7) case.
Power Residues of Fourier Coefficients of Modular Forms
Authors: Weston Tom 
Published: December 2010

AbstractLet ρ: GQ → GLn(Qℓ) be a motivic ℓ-adic Galois representation. For fixed m > 1 we initiate an investigation of the density of the set of primes p such that the trace of the image of an arithmetic Frobenius at p under ρ is an m-th power residue modulo p. Based on numerical investigations with modular forms we conjecture (with Ramakrishna) that this density equals 1/m whenever the image of ρ is open. We further conjecture that for such ρ the set of these primes p is independent of any set defined by Cebatorev-style Galois-theoretic conditions (in an appropriate sense). We then compute these densities for certain m in the complementary case of modular forms of CM-type with rational Fourier coefficients; our proofs are a combination of the Cebatorev density theorem(which does apply in the CM case) and reciprocity laws applied to Hecke characters. We also discuss a potential application (suggested by Ramakrishna) to computing inertial degrees at p in abelian extensions of imaginary quadratic fields unramified away from p.
Some Conditions for Decay of Convolution Powers and Heat Kernels on Groups
Authors: Dungey Nick 
Published: December 2010

AbstractLetKbe a function on a unimodular locally compact groupG, and denote byKn=K*K* · · · *Kthen-th convolution power ofK. Assuming thatKsatisfies certain operator estimates inL2(G), we give estimates of the normsandfor largen. In contrast to previous methods for estimating, we do not need to assume that the functionKis a probability density or nonnegative. Our results also adapt for continuous time semigroups onG. Various applications are given, for example, to estimates of the behaviour of heat kernels on Lie groups.
Relative Darboux Theorem for Singular Manifolds and Local Contact Algebra
Authors: Zhitomirskii M. 
Published: December 2010

AbstractIn 1999 V. Arnol’d introduced the local contact algebra: studying the problem of classification of singular curves in a contact space, he showed the existence of the ghost of the contact structure (invariants which are not related to the induced structure on the curve). Our main result implies that the only reason for existence of the local contact algebra and the ghost is the difference between the geometric and (defined in this paper) algebraic restriction of a 1-form to a singular submanifold. We prove that a germ of any subset N of a contact manifold is well defined, up to contactomorphisms, by the algebraic restriction to N of the contact structure. This is a generalization of the Darboux-Givental’ theoremfor smooth submanifolds of a contactmanifold. Studying the difference between the geometric and the algebraic restrictions gives a powerful tool for classification of stratified submanifolds of a contact manifold. This is illustrated by complete solution of three classification problems, including a simple explanation of V. Arnold's results and further classification results for singular curves in a contact space. We also prove several results on the external geometry of a singular submanifold N in terms of the algebraic restriction of the contact structure to N. In particular, the algebraic restriction is zero if and only if N is contained in a smooth Legendrian submanifold of M.
C*-Algebras of Irreversible Dynamical Systems
Authors: Exel R. , Vershik A. 
Published: December 2010

AbstractWe show that certain C*-algebras which have been studied by, among others, Arzumanian, Vershik, Deaconu, and Renault, in connection with a measure-preserving transformation of a measure space or a covering map of a compact space, are special cases of the endomorphism crossed product construction recently introduced by the first named author. As a consequence these algebras are given presentations in terms of generators and relations. These results come as a consequence of a general theorem on faithfulness of representations which are covariant with respect to certain circle actions. For the case of topologically free covering maps we prove a stronger result on faithfulness of representations which needs no covariance. We also give a necessary and sufficient condition for simplicity.
Infinite Dimensional Representations of Canonical Algebras
Authors: Reiten Idun , Ringel Claus Michael 
Published: December 2010

AbstractThe aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to themore general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with canonical algebras. The investigation is centered around the generic and the Prüfer modules, and how other modules are determined by these modules.
Stark's Conjecture and New Stickelberger Phenomena
Authors: Snaith Victor P. 
Published: December 2010

AbstractWe introduce a new conjecture concerning the construction of elements in the annihilator ideal associated to a Galois action on the higher-dimensional algebraicK–groups of rings of integers in number fields. Our conjecture ismotivic in the sense that it involves the (transcendental) Borel regulator as well as being related tol–adic étale cohomology. In addition, the conjecture generalises the wellknown Coates–Sinnott conjecture. For example, for a totally real extension whenr= –2,–4,–6, … the Coates–Sinnott conjecturemerely predicts that zero annihilatesK–2rof the ring ofS–integers while our conjecture predicts a non-trivial annihilator. By way of supporting evidence, we prove the corresponding (conjecturally equivalent) conjecture for the Galois action on the étale cohomology of the cyclotomic extensions of the rationals.
On the Group of Homeomorphisms of the Real Line That Map the Pseudoboundary Onto Itself
Authors: Dijkstra Jan J. , Mill Jan van 
Published: December 2010

AbstractIn this paper we primarily consider two natural subgroups of the autohomeomorphism group of the real line ℝ, endowed with the compact-open topology. First, we prove that the subgroup of homeomorphisms that map the set of rational numbers ℚ onto itself is homeomorphic to the infinite power of ℚ with the product topology. Secondly, the group consisting of homeomorphisms that map the pseudoboundary onto itself is shown to be homeomorphic to the hyperspace of nonempty compact subsets of ℚ with the Vietoris topology. We obtain similar results for the Cantor set but we also prove that these results do not extend to ℝn for n ≥ 2, by linking the groups in question with Erdős space.
Annihilators for the Class Group of a Cyclic Field of Prime Power Degree, II
Authors: Greither Cornelius , Kučera Radan 
Published: December 2010

AbstractWe prove, for a field K which is cyclic of odd prime power degree over the rationals, that the annihilator of the quotient of the units of K by a suitable large subgroup (constructed from circular units) annihilates what we call the non-genus part of the class group. This leads to stronger annihilation results for the whole class group than a routine application of the Rubin–Thaine method would produce, since the part of the class group determined by genus theory has an obvious large annihilator which is not detected by that method; this is our reason for concentrating on the non-genus part. The present work builds on and strengthens previous work of the authors; the proofs are more conceptual now, and we are also able to construct an example which demonstrates that our results cannot be easily sharpened further.