bluuebunny/crossref_metadata_2025_split huggingface dataset:
Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains
Authors: Edward Julian 
Published: December 2010

AbstractThe growth properties at infinity for eigenfunctions corresponding to embedded eigenvalues of the Neumann Laplacian on horn-like domains are studied. For domains that pinch at polynomial rate, it is shown that the eigenfunctions vanish at infinity faster than the reciprocal of any polynomial. For a class of domains that pinch at an exponential rate, weaker, L2 bounds are proven. A corollary is that eigenvalues can accumulate only at zero or infinity.
Perfect Non-Extremal Riemann Surfaces
Authors: Schaller Paul Schmutz 
Published: December 2010

AbstractAn infinite family of perfect, non-extremal Riemann surfaces is constructed, the first examples of this type of surfaces. The examples are based on normal subgroups of the modular group PSL(2, ℤ) of level 6. They provide non-Euclidean analogues to the existence of perfect, non-extremal positive definite quadratic forms. The analogy uses the function syst which associates to every Riemann surface M the length of a systole, which is a shortest closed geodesic of M.
The Inequalities for Polynomials and Integration over Fractal Arcs
Authors: Kats B. A. 
Published: December 2010

AbstractThe paper is dealing with determination of the integral along the fractal arc γ on the complex plane by terms of polynomial approximations of the function ƒ. We obtain inequalities for polynomials and conditions of integrability for functions from the Hölder, Besov and Slobodetskii spaces.
Linéarisation symplectique en dimension 2
Authors: Currás-Bosch Carlos 
Published: December 2010

AbstractIn this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is , the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.
Weak Convergence Is Not Strong Convergence For Amenable Groups
Authors: Rosenblatt Joseph M. , Willis George A. 
Published: December 2010

AbstractLet G be an infinite discrete amenable group or a non-discrete amenable group. It is shown how to construct a net (fα) of positive, normalized functions in L1(G) such that the net converges weak* to invariance but does not converge strongly to invariance. The solution of certain linear equations determined by colorings of the Cayley graphs of the group are central to this construction.
Inductive Limit Toral Automorphisms of Irrational Rotation Algebras
Authors: Stacey P. J. 
Published: December 2010

AbstractIrrational rotation C*-algebras have an inductive limit decomposition in terms of matrix algebras over the space of continuous functions on the circle and this decomposition can be chosen to be invariant under the flip automorphism. It is shown that the flip is essentially the only toral automorphism with this property.
A Hypergraph with Commuting Partial Laplacians
Authors: Ballantine Cristina M. 
Published: December 2010

AbstractLetFbe a totally real number field and let GLnbe the general linear group of rank n overF. Let р be a prime ideal ofFand Fрthe completion ofFwith respect to the valuation induced by р. We will consider a finite quotient of the affine building of the group GLnover the field Fр. We will view this object as a hypergraph and find a set of commuting operators whose sum will be the usual adjacency operator of the graph underlying the hypergraph.
Uniform Embeddings into Hilbert Space and a Question of Gromov
Authors: Dranishnikov A. N. , Gong G. , Lafforgue V. , Yu G. 
Published: December 2010

AbstractGromov introduced the concept of uniform embedding into Hilbert space and asked if every separable metric space admits a uniform embedding into Hilbert space. In this paper, we study uniform embedding into Hilbert space and answer Gromov’s question negatively.
The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X5 + aX + b
Authors: Spearman Blair K. , Williams Kenneth S. 
Published: December 2010

AbstractLet X5 + aX + b ∈ Z[X] have Galois group D5. Let θ be a root of X5 + aX + b. An explicit formula is given for the discriminant of Q(θ).
Sur les singularités de la fonction croissance d’une variété non simplement connexe
Authors: Ardizzone Lucia , Grimaldi Renata , Pansu Pierre 
Published: December 2010

RésuméSi M est une variété de dimension n, compacte non simplement connexe, on caractérise les métriques riemanniennes sur M dont la fonction croissance a exactement deux singularités.
A Note on the Automorphic Langlands Group
Authors: Arthur James 
Published: December 2010

AbstractLanglands has conjectured the existence of a universal group, an extension of the absolute Galois group, which would play a fundamental role in the classification of automorphic representations. We shall describe a possible candidate for this group. We shall also describe a possible candidate for the complexification of Grothendieck's motivic Galois group.
Group Gradings on Matrix Algebras
Authors: Bahturin Yu. A. , Zaicev M. V. 
Published: December 2010

AbstractLet Φ be an algebraically closed field of characteristic zero, G a finite, not necessarily abelian, group. Given a G-grading on the full matrix algebra A = Mn(Φ), we decompose A as the tensor product of graded subalgebras A = B ⊗ C, B ≅ Mp(Φ) being a graded division algebra, while the grading of C ≅ Mq(Φ) is determined by that of the vector space Φn. Now the grading of A is recovered from those of A and B using a canonical “induction” procedure.
Subalgebras of gcN and Jacobi Polynomials
Authors: De Sole Alberto , Kac Victor G. 
Published: December 2010

AbstractWe classify the subalgebras of the general Lie conformal algebra gcN that act irreducibly on [∂]N and that are normalized by the sl2-part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials , σ ∈ . The connection goes both ways—we use in our classification some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.
Properties of the ℳ-Harmonic Conjugate Operator
Authors: Lee Jaesung , Rim Kyung Soo 
Published: December 2010

AbstractWe define the ℳ-harmonic conjugate operator K and prove that it is bounded on the nonisotropic Lipschitz space and on BMO. Then we show K maps Dini functions into the space of continuous functions on the unit sphere. We also prove the boundedness and compactness properties of ℳ-harmonic conjugate operator with Lp symbol.
The Ramification Polygon for Curves over a Finite Field
Authors: Scherk John 
Published: December 2010

AbstractA Newton polygon is introduced for a ramified point of a Galois covering of curves over a finite field. It is shown to be determined by the sequence of higher ramification groups of the point. It gives a blowing up of the wildly ramified part which separates the branches of the curve. There is also a connection with local reciprocity.
Classification of AF Flows
Authors: Dean Andrew J. 
Published: December 2010

AbstractAn AF flow is a one-parameter automorphism group of an AFC*-algebraAsuch that there exists an increasing sequence of invariant finite dimensional sub-C*-algebras whose union is dense inA. In this paper, a classification ofC*-dynamical systems of this form up to equivariant isomorphism is presented. Two pictures of the actions are given, one in terms of a modified Bratteli diagram/pathspace construction, and one in terms of a modifiedK0functor.
Counting the Number of Integral Points in General n-Dimensional Tetrahedra and Bernoulli Polynomials
Authors: Lin Ke-Pao , Yau Stephen S.-T. 
Published: December 2010

AbstractRecently there has been tremendous interest in counting the number of integral points in n-dimensional tetrahedra with non-integral vertices due to its applications in primality testing and factoring in number theory and in singularities theory. The purpose of this note is to formulate a conjecture on sharp upper estimate of the number of integral points in n-dimensional tetrahedra with non-integral vertices. We show that this conjecture is true for low dimensional cases as well as in the case of homogeneous n-dimensional tetrahedra. We also show that the Bernoulli polynomials play a role in this counting.
Reducing Spheres and Klein Bottles after Dehn Fillings
Authors: Oh Seungsang 
Published: December 2010

AbstractLet M be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on M along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.
Characterizing Two-Dimensional Maps Whose Jacobians Have Constant Eigenvalues
Authors: Chamberland Marc 
Published: December 2010

AbstractRecent papers have shown that C1 maps whose Jacobians have constant eigenvalues can be completely characterized if either the eigenvalues are equal or F is a polynomial. Specifically, F = (u, v) must take the formfor some constants a, b, c, d, e, f , α, β and a C1 function ϕ in one variable. If, in addition, the function ϕ is not affine, thenThis paper shows how these theorems cannot be extended by constructing a real-analytic map whose Jacobian eigenvalues are ±1/2 and does not fit the previous form. This example is also used to construct non-obvious solutions to nonlinear PDEs, including the Monge—Ampère equation.
Gauss and Eisenstein Sums of Order Twelve
Authors: Gurak S. 
Published: December 2010

AbstractLet q = pr with p an odd prime, and Fq denote the finite field of q elements. Let Tr : Fq → Fp be the usual trace map and set ζp = exp(2πi/p). For any positive integer e, define the (modified) Gauss sum gr(e) byRecently, Evans gave an elegant determination of g1(12) in terms of g1(3), g1(4) and g1(6) which resolved a sign ambiguity present in a previous evaluation. Here I generalize Evans' result to give a complete determination of the sum gr(12).
On Density Conditions for Interpolation in the Ball
Authors: Marco Nicolas , Massaneda Xavier 
Published: December 2010

AbstractIn this paper we study interpolating sequences for two related spaces of holomorphic functions in the unit ball of Cn, n > 1. We first give density conditions for a sequence to be interpolating for the class A−∞ of holomorphic functions with polynomial growth. The sufficient condition is formally identical to the characterizing condition in dimension 1, whereas the necessary one goes along the lines of the results given by Li and Taylor for some spaces of entire functions. In the second part of the paper we show that a density condition, which for n = 1 coincides with the characterizing condition given by Seip, is sufficient for interpolation in the (weighted) Bergman space.
On Universal Schauder Bases in Non-Archimedean Fréchet Spaces
Authors: Śliwa Wiesław 
Published: December 2010

AbstractIt is known that any non-archimedean Fréchet space of countable type is isomorphic to a subspace of . In this paper we prove that there exists a non-archimedean Fréchet space U with a basis (un) such that any basis (xn) in a non-archimedean Fréchet space X is equivalent to a subbasis (ukn) of (un). Then any non-archimedean Fréchet space with a basis is isomorphic to a complemented subspace of U. In contrast to this, we show that a non-archimedean Fréchet space X with a basis (xn) is isomorphic to a complemented subspace of if and only if X is isomorphic to one of the following spaces: c0, c0 × . Finally, we prove that there is no nuclear non-archimedean Fréchet space H with a basis (hn) such that any basis (yn) in a nuclear non-archimedean Fréchet space Y is equivalent to a subbasis (hkn) of (hn).
Embeddability of Some Three-Dimensional Weakly Pseudoconvex CR Structures
Authors: Wang Wei 
Published: December 2010

AbstractWe prove that a class of perturbations of standard CR structure on the boundary of threedimensional complex ellipsoid Ep, q can be realized as hypersurfaces on ℂ2, which generalizes the result of Burns and Epstein on the embeddability of some perturbations of standard CR structure on S3.
On the Uniqueness of Wave Operators Associated with Non-Trace Class Perturbations
Authors: Xia Jingbo 
Published: December 2010

AbstractVoiculescu has previously established the uniqueness of the wave operator for the problem of -perturbation of commuting tuples of self-adjoint operators in the case where the norm ideal has the property , where {Pn} is any sequence of orthogonal projections with rank(Pn) = n. We prove that the same uniqueness result holds true so long as is not the trace class. (It is well known that there is no such uniqueness in the case of trace-class perturbation.)
A Geometric Approach to Voiculescu-Brown Entropy
Authors: Kerr David 
Published: December 2010

AbstractA basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are “chaotic.” While there is a vast collection of results addressing this issue in topological dynamics, the phenomenon of positive entropy remains by and large a mystery within the broader noncommutative domain of C*-algebraic dynamics. To shed some light on the noncommutative situation we propose a geometric perspective inspired by work of Glasner and Weiss on topological entropy. This is a written version of the author’s talk at theWinter 2002Meeting of the CanadianMathematical Society in Ottawa, Ontario.
Degree Homogeneous Subgroups
Authors: Dixon John D. , Barghi A. Rahnamai 
Published: December 2010

AbstractLet G be a finite group and H be a subgroup. We say that H is degree homogeneous if, for each χ ∈ Irr(G), all the irreducible constituents of the restriction χH have the same degree. Subgroups which are either normal or abelian are obvious examples of degree homogeneous subgroups. Following a question by E.M. Zhmud’, we investigate general properties of such subgroups. It appears unlikely that degree homogeneous subgroups can be characterized entirely by abstract group properties, but we providemixed criteria (involving both group structure and character properties) which are both necessary and sufficient. For example, H is degree homogeneous in G if and only if the derived subgroup H′ is normal in G and, for every pair α, β of irreducible G-conjugate characters of H′, all irreducible constituents of αH and βH have the same degree.
Products of Conjugacy Classes in SU(2)
Authors: Jeffrey Lisa C. , Mare Augustin-Liviu 
Published: December 2010

AbstractWe obtain a complete description of the conjugacy classes C1, … ,Cn in SU(2) with the property that C1 … Cn = SU(2). The basic instrument is a characterization of the conjugacy classes C1, … ,Cn+1 in SU(2) with C1 … Cn+1 ∋ I, which generalizes a result of [Je-We].
On Negatively Curved Finsler Manifolds of Scalar Curvature
Authors: Mo Xiaohuan , Shen Zhongmin 
Published: December 2010

AbstractIn this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimensionn≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.
Baker-Type Estimates for Linear Forms in the Values of q-Series
Authors: Väänänen Keijo , Zudilin Wadim 
Published: December 2010

AbstractWe obtain lower estimates for the absolute values of linear forms of the values of generalized Heine series at non-zero points of an imaginary quadratic field II, in particular of the values of q-exponential function. These estimates depend on the individual coefficients, not only on the maximum of their absolute values. The proof uses a variant of classical Siegel's method applied to a system of functional Poincaré-type equations and the connection between the solutions of these functional equations and the generalized Heine series.
The Index Theory Associated to a Non-Finite Trace on a C*-Algebra
Authors: Murphy G. J. 
Published: December 2010

AbstractThe index theory considered in this paper, a generalisation of the classical Fredholm index theory, is obtained in terms of a non-finite trace on a unitalC*-algebra. We relate it to the index theory of M. Breuer, which is developed in a von Neumann algebra setting, by means of a representation theorem. We show how our new index theory can be used to obtain an index theorem for Toeplitz operators on the compact group U(2), where the classical index theory does not give any interesting result.
On Gâteaux Differentiability of Convex Functions in WCG Spaces
Authors: Rychtář Jan 
Published: December 2010

AbstractIt is shown, using the Borwein–Preiss variational principle that for every continuous convex function f on a weakly compactly generated space X, every x0 ∈ X and every weakly compact convex symmetric set K such that , there is a point of Gâteaux differentiability of f in x0 +K. This extends a Klee's result for separable spaces.
B-Stable Ideals in the Nilradical of a Borel Subalgebra
Authors: Sommers Eric N. 
Published: December 2010

AbstractWe count the number of strictly positive B-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any B-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.
A Note on Lagrangian Loci of Quotients
Authors: Foth Philip 
Published: December 2010

AbstractWe study Hamiltonian actions of compact groups in the presence of compatible involutions. We show that the Lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a given real form can be reduced to the quasi-split real form in the same inner class. We also consider invariant quotients with respect to the corresponding real form of the complexified group.
On a Theorem of Kawamoto on Normal Bases of Rings of Integers, II
Authors: Ichimura Humio 
Published: December 2010

AbstractLet m = pe be a power of a prime number p. We say that a number field F satisfies the property when for any a ∈ F×, the cyclic extension F(ζm, a1/m)/F(ζm) has a normal p-integral basis. We prove that F satisfies if and only if the natural homomorphism is trivial. Here K = F(ζm), and denotes the ideal class group of F with respect to the p-integer ring of F.
On a Class of Singular Integral Operators With Rough Kernels
Authors: Al-Salman Ahmad 
Published: December 2010

AbstractIn this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.
On the Inequality for Volume and Minkowskian Thickness
Authors: Averkov Gennadiy 
Published: December 2010

AbstractGiven a centrally symmetric convex bodyBin, we denote by ℳd(B) the Minkowski space (i.e., finite dimensional Banach space) with unit ballB. LetKbe an arbitrary convex body in ℳd(B). The relationship between volumeV(K) and the Minkowskian thickness (= minimal width) ΔB(K) ofKcan naturally be given by the sharp geometric inequalityV(K) ≥ α(B) · ΔB(K)d, where α(B) > 0. As a simple corollary of the Rogers-Shephard inequality we obtain thatwith equality on the left attained if and only ifBis the difference body of a simplex and on the right ifBis a cross-polytope. The main result of this paper is that ford= 2 the equality on the right implies thatBis a parallelogram. The obtained results yield the sharp upper bound for the modified Banach–Mazur distance to the regular hexagon.
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain
Authors: Girela Daniel , Peláez José Ángel 
Published: December 2010

AbstractIt is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces Ap with 0 < p < 3/2. The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products B with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of B′ in the space Ap (p < 1). As a consequence, we prove that there exists a Blaschke product B with zeros on a radius such that B′ ∉ A3/2.
A Singular Critical Potential for the Schrödinger Operator
Authors: Duyckaerts Thomas 
Published: December 2010

AbstractConsider a real potential V on Rd, d ≥ 2, and the Schrödinger equation:(LS) i∂tu + Δu −Vu = 0, u↾t=0 = u0 ∈ L2.In this paper, we investigate the minimal local regularity of V needed to get local in time dispersive estimates (such as local in time Strichartz estimates or local smoothing effect with gain of 1/2 derivative) on solutions of (LS). Prior works show some dispersive properties when V (small at infinity) is in Ld/2 or in spaces just a little larger but with a smallness condition on V (or at least on its negative part).In this work, we prove the critical character of these results by constructing a positive potential V which has compact support, bounded outside 0 and of the order (log |x|)2/|x|2 near 0. The lack of dispersiveness comes from the existence of a sequence of quasimodes for the operator P := −Δ + V.The elementary construction of V consists in sticking together concentrated, truncated potential wells near 0. This yields a potential oscillating with infinite speed and amplitude at 0, such that the operator P admits a sequence of quasi-modes of polynomial order whose support concentrates on the pole.
On the Lack of Inverses to C*-Extensions Related to Property T Groups
Authors: Manuilov V. , Thomsen K. 
Published: December 2010

AbstractUsing ideas of S. Wassermann on non-exact C*-algebras and property T groups, we show that one of his examples of non-invertible C*-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a C*-extension which is not even invertible up to homotopy.