bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Hankel and Some Related Transformations
Authors: Heywood P. , Rooney P. G. 
Published: December 2010

The transformations we will discuss in this paper are the Hankel
transformation Hυ
defined for f ∊ C
0, the collection of continuous functions compactly supported
in (0, ∞), by

(1.1)

and the and
transformations
defined for such f by

(1.2)

and

(1.3)

where Jv
&gt;and Yv
are the Bessel functions of the first and second kinds
respectively, and H

v
is the Struve function; for the theory of these functions see
[1, Chapter VII].
These transformations were studied extensively by one of us in
[5] and [6] on the spaces
defined in
[7; Sections 1 &amp; 5]. In those papers the
boundedness of the three transformations was fully given on the spaces
for 1 &lt;
p &lt; ∞, but not for
p = 1. Also inversion formulae were given for the
transformations only for portions of their respective ranges of
boundedness.
On the Askey-Wilson and Rogers Polynomials
Authors: Ismail Mourad E. H. , Stanton Dennis 
Published: December 2010

The q-shifted factorial (a)n or (a; q)n isand an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials1.1where1.2and1.3We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 polynomials. They generalize the 6 — j symbols and are the most general classical orthogonal polynomials, [2].
On the Existence of Positive Decaying Entire Solutions for a Class of Sublinear Elliptic Equations
Authors: Furusho Yasuhiro , Kusano Takaŝi 
Published: December 2010

In recent years there has been a growing interest in the existence and asymptotic behavior of entire solutions for second order nonlinear elliptic equations. By an entire solution we mean a solution of the elliptic equation under consideration which is guaranteed to exist in the whole Euclidean N-space RN, N ≧ 2. For standard results on the subject the reader is referred to the papers [2-7, 9-21].The study of entire solutions, which at an early stage was restricted to simple equations of the form Δu + f(x, u) = 0, x ∊ RN, Δ being the N-dimensional Laplacian, has now been extended and generalized to elliptic equations of the typeAwhere
On VMOA for Riemann Surfaces
Authors: Aulaskari Rauno 
Published: December 2010

Let Δ = {z│ │z│ < 1} be the unit disk and f an analytic function in Δ. The Dirichlet integral DΔ(f) of f on Δ is defined byand we denote by AD(Δ) the space of all functions f analytic on Δ for which DΔ(f) < ∞. We denote by BMOA(Δ) the space of analytic functions f in Δ for whichand by VMOA(Δ) the space of those analytic functions f in BMOA(Δ) satisfying the condition
Existence of Positive Global Solutions of Mixed Sublinear-Superlinear Problems
Authors: Allegretto W. , Huang Y. X. 
Published: December 2010

Consider the elliptic quasilinear problem:1in Rn, n ≧ 3, whereWe are interested in establishing sufficient conditions on f for the existence of positive solutions u(x) with specified behaviour at ∞. Of special interest to us are criteria which guarantee that u(x) decays at least as fast as |x|−α for some α ≧ 0, given below, in the case f(x, u, ∇u) contains terms of typeThat is: f is of mixed sublinear-super linear type. Our main result is Theorem 3 below which explicitly states sufficient conditions for the existence of such solutions.
Spherical Homology Classes in the Bordism of Lie Groups
Authors: Kane Richard , Moreno Guillermo 
Published: December 2010

The mod torsion Hurewicz mapfor compact Lie groups provides a useful and efficient means of studying G. In effect, it measures how far G fails to be a product of spheres. For the Hopf-Samelson theorem (see [17]) tells us thatIn other wordsSerre pointed out that there exists a mapinducing this Q isomorphism.
Uniform Harmonic Approximation with Continuous Extension to the Boundary
Authors: Goldstein M. , Ow W. H. 
Published: December 2010

Let G be a domain in the complex plane and F a nonempty subset of G such that F is the closure in G of its interior F0. We will say f ∊ C1(F) if f is continuous on F and possesses continuous first partial derivatives in F which extend continuously to F as finite-valued functions. Let G* – F be connected and locally connected, f ∊ C1(F) be harmonic in F0, and E be a subset of ∂F ∩ ∂G (here G* denotes the one-point compactification of G and the boundaries ∂F, ∂G are taken in the extended plane). Suppose there is a sequence 〈hn〉 of functions harmonic in G such thatuniformly on F as n → ∞.
On the Essential Spectra of Quasisimilar Operators
Authors: Herrero Domingo A. 
Published: December 2010

B. Sz.-Nagy and C. Foiaş gave the first examples of quasisimilar operators with different spectra [25]. Indeed, quasisimilar operators can even have different spectral radius [19] (see also [15]). Nevertheless, T. B. Hoover has shown in [19] that if T and S are quasisimilar, then σ(T)∩σ(S) ≠ ∅, where σ(R) denotes the spectrum of the (bounded linear) operator R. In [12], the author improved Hoover's result by showing that each component of σ(S) intersects σ(T), and viceversa. This, in turn, was further improved by L. A. Fialkow in [7]. (Actually, Fialkow's results were obtained independently of [12].)L. A. Fialkow [7] and L. R. Williams [27] independently proved that σe(T)∩σe(S) ≠ ∅, where σe(R) denotes the essential spectrum of R. Several authors have raised the following natural question:Is it also true that each component of σe(S) intersects σe(T), and viceversa? [7] [21] [26].
Homomorphisms Between Algebras of Continuous Functions
Authors: Llavona J. G. , Jaramillo J. A. 
Published: December 2010

We are concerned in this paper with the study of homomorphisms between different algebras of continuous functions, especially the algebras of real functions which are either weakly continuous on bounded sets or weakly uniformly continuous on bounded sets on a Banach space (see definitions below).These spaces of weakly [uniformly] continuous functions appeared in relation with some questions in Infinite-dimensional Approximation Theory (see [4], [6], [11], [12], [13] and [16]); and since the structure of these function spaces is closely related with properties of different weak topologies (the bounded-weak and bounded-weak* topologies, respectively) and with the structure of Banach spaces on which they are defined, their study also presents interest from the point of view of Banach space theory, as can be seen in [2], [12] or [17].
Homogeneous Complex Manifolds with more than One End
Authors: Gilligan B. , Oeljeklaus K. , Richthofer W. 
Published: December 2010

For homogeneous spaces of a (real) Lie group one of the fundamental results concerning ends (in the sense of Freudenthal [8] ) is due to A. Borel [6]. He showed that if X = G/H is the homogeneous space of a connected Lie group G by a closed connected subgroup H, then X has at most two ends. And if X does have two ends, then it is diffeomorphic to the product of R with the orbit of a maximal compact subgroup of G.In the setting of homogeneous complex manifolds the basic idea should be to find conditions which imply that the space has at most two ends and then, when the space has exactly two ends, to display the ends via bundles involving C* and compact homogeneous complex manifolds. An analytic condition which ensures that a homogeneous complex manifold X has at most two ends is that X have non-constant holomorphic functions and the structure of such a space with exactly two ends is determined, namely, it fibers over an affine homogeneous cone with its vertex removed with the fiber being compact [9], [13].
Plane Curves With Nodes
Authors: Treger Robert 
Published: December 2010

A smooth algebraic curve is birationally equivalent to a nodal plane curve. One of the main problems in the theory of plane curves is to describe the situation of nodes of an irreducible nodal plane curve (see [16, Art. 45], [10], [7, Book IV, Chapter I, §5], [12, p. 584], and [3]).Let n denote the degree of a nodal curve and d the number of nodes. The case (AZ, d) — (6,9) has been analyzed by Halphen [10]. It follows from Lemma 3.5 and Proposition 3.6 that this is an exceptional case. The case d ≦n(n + 3)/6, d ≦(n — 1)(n — 2)/2, and (n, d) ≠ (6,9) was investigated by Arbarello and Cornalba [3]. We present a simpler proof (Corollary 3.8).We consider the main case which is particularly important due to its applications to the moduli variety of curves, compare [19, Chapter VIII, Section 4]. Let Vn,d be the variety of irreducible curves of degree n with d nodes and no other singularities such that each curve of Vn,d can be degenerated into n lines in general position (see [17]).
A Mixed Parseval's Equation And a Generalized Hankel Transformation of Distributions
Authors: Betancor J. J. 
Published: December 2010

Let an integral transform T﹛f﹜ of a complex valued function f(x) defined over the interval (0, ∞) be defined as One of the most usual procedures to extend the classical transform (l.a) to generalized functions consists in constructing a space A of testing functions over (0, ∞) which is closed with respect to the classical transform (l.a) and then the corresponding transform of the generalized function/ of the dual space of A is defined through This approach has been followed by L. Schwartz [13] and A. H. Zemanian [20], amongst others.
Composition with a Nonhomogeneous Bounded Holomorphic Function on the Ball
Authors: Choa Jun Soo , Kim Hong Oh 
Published: December 2010

For an integer n > 1, the letters U and Bn denote the open unit disc in C and the open euclidean unit ball in Cn, respectively. It is known that the homogeneous polynomialswhere bα is chosen so that , have the following pull-back property:If g ∈ ℬ(U) the Block space, then , the space of holomorphic functions on Bn of bounded mean oscillation, forand.
Sur le Socle Dans Les Algèbres de Jordan-Banach
Authors: Aupetit Bernard , Baribeau Line 
Published: December 2010

Dans une algèbre de Banach, le socle joue le même rôle que l'ensemble des opérateurs de rang fini dans le cas de l'algèbre des opérateurs linéaires continus sur un espace de Banach. Aussi est-il intéressant de savoir dans quels cas le socle n'est pas réduit à zéro.En 1968, B. A. Barnes ([6], Théorème 2.1 et Théorème 2.2) a pu démontrer le théorème suivant:Théorème 1. Soit A une algèbre de Banach complexe sans radical. Supposonsque le spectre de chaque élément de A est dénombrable. Alors le socle de A estnon nul.
Generalized Newton-Puiseux Theory and Hensel's Lemma in C[[x, y]]
Authors: Kuo Tzee-Char 
Published: December 2010

The Newton polygon and the Newton-Puiseux algorithm ([3], p. 370, [8], p. 98), and their generalizations, serve as a powerful tool for analysing the singularities of a given function. Yet experts know how difficult it is to keep track of them when one, or several, blowing-ups are applied. Thus many interesting theorems are stated under the strong, rather undesirable, assumption that the Newton faces are non-degenerate.In this paper, we introduce a method which is parallel to the classical Newton-Puiseux theory, yet avoids blowing-ups and fractional power series, except in the proofs.
Diameters in Typical Convex Bodies
Authors: Bárány Imre , Zamfirescu Tudor 
Published: December 2010

The most usual diameters in the world are those of a sphere and they all contain its centre. More generally, a chord of a convex body in Rd is called a diameter if there are two parallel supporting hyperplanes at the two endpoints of the chord.It is easily seen that there are points on at least two diameters. From a result of Kosiński [6] proved in a more general setting it follows that every convex body has a point lying on at least three diameters. Does a typical convex body behave like a sphere and contain a point on infinitely or even uncountably many diameters?But what is a typical convex body? The space 𝒦 of all convex bodies (d-dimensional compact convex sets) in Rd, equipped with the Hausdorff metric, is a Baire space.
Resolubilite Local Pour des Equations Semi Lineaires Complexes
Authors: Dehman B. 
Published: December 2010

Dans ce travail, nous construisons des solutions pour une certaine classe d'équations semi-linéaires complexes dans le plan. Plus précisément on considère prés d'un point XQde R2 l'équation où Pest un opérateur différentiel d'ordre m(m≧ 1) à coefficients C∞ complexes, et o ù ƒest à valeurs complexes, analytique en et seulement C∞ en x.En supposant alors que Pest de type principal près de xoet vérifie la condition de Nirenberg-Trêves sous elliptique (que nous noterons ((P), voir [5]), nous construisons une solution locale de (*), de classe C∞ (Théorème 2.1).Ce résultat échappe évidemment aux théorèmes classiques d'existence de Hamilton-Jacobi et de Cauchy-Kowalevsky.
Universal Varieties Of (0, 1)-Lattices
Authors: Goralčík P. , Koubek V. , Sichler J. 
Published: December 2010

This article fully characterizes categorically universal varieties of (0, 1)-lattices (that is, lattices with a least element 0 and a greatest element 1 regarded as nullary operations), thereby concluding a series of partial results [3, 5, 8, 10, also 14] which originated with the proof of categorical universality for the variety of all (0, 1)-lattices by Grätzer and Sichler [6].A category C of algebras of a given type is universal if every category of algebras (and equivalently, according to Hedrlín and Pultr [7 or 14], also the category of all graphs) is isomorphic to a full subcategory of C. The universality of C is thus equivalent to the existence of a full embedding Φ : G→C of the category G of all graphs and their compatible mappings into C. When Φ assigns a finite algebra to every finite graph, we say that C is finite-to-finite universal.
Functional Equations, Distributions and Approximate Identities
Authors: Baker John A. 
Published: December 2010

The subject of this paper is the use of the theory of Schwartz distributions and approximate identities in studying the functional equationThe aj’s and b are complex-valued functions defined on a neighbourhood, U, of 0 in Rm, hj. U → Rn with hj(0) = 0 and fj, g: Rn → C for 1 ≦ j ≦ N. In most of what follows the aj's and hj's are assumed smooth and may be thought of as given. The fj‘s, b and g may be thought of as the unknowns. Typically we are concerned with locally integrable functions f1, … , fN such that, for each s in U, (1) holds for a.e. (almost every) x ∈ Rn, in the sense of Lebesgue measure.
Representation Formulas for Integrable and Entire Functions of Exponential Type II
Authors: Frappier Clément 
Published: December 2010

We adopt the terminology and notations of [5]. If f ∈ Bτ is an entire function of exponential type τ bounded on the real axis then we have the complementary interpolation formulas [1, p. 142-143] andwhere t, γ are reals and
Berg's Technique for Pseudo-Actions With Applications to af Embeddings
Authors: Loring Terry A. 
Published: December 2010

AbstractBerg's interchange technique is generalized to the context of certain new objects called pseudo-actions. This is used to find a more geometric proof of the Pimsner-Voiculescu theorem on the AF embedding of the irrational rotation algebras. Connections with Berg's original results are briefly examined.Embedding diagrams are introduced to provide a uniform way of describing embeddings of transformation group C*-algebras C(X) ⋊ ℤ into AF algebras. Pimsner has classified the transformation group C* -algebras which can be AF embedded. We present a new proof of this result using embedding diagrams and pseudo-actions. The need to calculate the join of an open cover with its iterates under the transformation has been eliminated.
Multidimensional Iterative Interpolation
Authors: Deslauriers Gilles , Dubois Jacques , Dubuc Serge 
Published: December 2010

AbstractWe define an iterative interpolation process for data spread over a closed discrete subgroup of the Euclidean space. We describe the main algebraic properties of this process. This interpolation process, under very weak assumptions, is always convergent in the sense of Schwartz distributions. We find also a convenient necessary and sufficient condition for continuity of each interpolation function of a given iterative interpolation process.
Scattering Theory And Spectral Representations For General Wave Equations With Short Range Perturbations
Authors: Yamamoto Kazuhiro 
Published: December 2010

AbstractIn this paper we shall develop the scattering theory introduced by Lax and Phillips [5] for the following general wave equation; where Ω is an exterior domain Rn(n ≥ 3) with the smooth boundary δΩ and B is either a Dirichlet boundary condition or of the form Bu = Vi(x)aij(x)δju+σ(x)u with the unit outer normal vector v(x) = (v1 , … , vn) at x ∈ δ Ω. The precise assumptions on α(x), aij(x),q(x), σ(x) are denoted below. If Ω is an inhomogeneous medium with the density ρ (x), the propagation of waves is described by (1.1) with a(x) = a(x)2 ρ(x), aij(x) = ρ-l(x) δij and q(x) = 0 with the velocity a(x).
Decaying Solutions Of 2mth Order Elliptic Problems
Authors: Allegretto W. , Yu L. S. 
Published: December 2010

AbstractWe consider a semilinear elliptic problem , (n > 2m). Under suitable conditions on f, we show the existence of a decaying positive solution. We do not employ radial arguments. Our main tools are weighted spaces, various applications of the Mountain Pass Theorem and LP regularity estimates of Agmon. We answer an open question of Kusano, Naito and Swanson [Canad. J. Math. 40(1988), 1281-1300] in the superlinear case: , and improve the results of Dalmasso [C. R. Acad. Sci. Paris 308(1989), 411-414] for the case .
Collision Local Times and Measure-Valued Processes
Authors: Barlow Martin T. , Evans Steven N. , Perkins Edwin A. 
Published: December 2010

AbstractWe consider two independent Dawson-Watanabe super-Brownian motions,Y1andY2. These processes are diffusions taking values in the space of finite measures on ℝd. We show that ifd ≤ 5then with positive probability there exist timestsuch that the closed supports ofintersect; whereas ifd> 5 then no such intersections occur. For the cased≤ 5, we construct a continuous, non-decreasing measure–valued processL(Y1,Y2), thecollision local time,such that the measure defined by, is concentrated on the set of times and places at which intersections occur. We give a Tanaka-like semimartingale decomposition ofL(Y1,Y2). We also extend these results to a certain class of coupled measurevalued processes. This extension will be important in a forthcoming paper where we use the tools developed here to construct coupled pairs of measure-valued diffusions withpoint interactions.In the course of our proofs we obtain smoothness results for the random measuresthat are uniform int.These theorems use a nonstandard description ofYiand are of independent interest.
Strong Boundedness and Strong Convergence in Sequence Spaces
Authors: Buntinas Martin , Tanović-Miller Naza 
Published: December 2010

AbstractStrong convergence has been investigated in summability theory and Fourier analysis. This paper extends strong convergence to a topological property of sequence spaces E. The more general property of strong boundedness is also defined and examined. One of the main results shows that for an FK-space E which contains all finite sequences, strong convergence is equivalent to the invariance property E = ℓ ν0. E with respect to coordinatewise multiplication by sequences in the space ℓν0 defined in the paper. Similarly, strong boundedness is equivalent to another invariance E = ℓν.E. The results of the paper are applied to summability fields and spaces of Fourier series.
Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
Authors: Lagarias Jeffrey C. , Ziegler Günter M. 
Published: December 2010

AbstractA lattice polytope is a polytope in whose vertices are all in . The volume of a lattice polytope P containing exactly k ≥ 1 points in d in its interior is bounded above by . Any lattice polytope in of volume V can after an integral unimodular transformation be contained in a lattice cube having side length at most n˙n ! V. Thus the number of equivalence classes under integer unimodular transformations of lattice poly topes of bounded volume is finite. If S is any simplex of maximum volume inside a closed bounded convex body K in having nonempty interior, then K⊆ ( n + 2)S — (n+ l)s where mS denotes a nomothetic copy of S with scale factor m, and s is the centroid of S.
Nilpotent Inner Derivations of the Skew Elements of Prime Rings With Involution
Authors: Martindale W. S. , Miers C. Robert 
Published: December 2010

AbstractLet R be a prime ring with invoution *, of characteristic 0, with skew elements K and extended centroid C. Let a ∈ K be such that (ad a)n =0 on K. It is shown that one of the following possibilities holds: (a) R is an order in a 4-dimensional central simple algebra, (b) there is a skew element λ in C such that , (c) * is of the first kind, n ≡ 0 or n ≡ 3 (mod 4), and . Examples are given illustrating (c).
On the Range and Invertibility of a Class of Melon Multiplier Transforms III
Authors: McBride A. C. , Spratt W. J. 
Published: December 2010

AbstractWe continue to develop the theory of previous papers concerning transforms corresponding to Mellin multipliers which involve products and/or quotients of Γ-functions. We show that, by working with certain subspaces of Lp,μ consisting of smooth functions, we can simplify considerably the restrictions on the parameters which were necessary in the Lp,μ setting. As a result, operators in our class become homeomorphisms on these subspaces under conditions of great generality.
Tensor Products of Operator Spaces II
Authors: Blecher David P. 
Published: December 2010

AbstractTogether with Vern Paulsen we were able to show that the elementary theory of tensor norms of Banach spaces carries over to operator spaces. We suggested that the Grothendieck tensor norm program, which was of course enormously important in the development of Banach space theory, be carried out for operator spaces. Some of this has been done by the authors mentioned above, and by Effros and Ruan. We give alternative developments of some of this work, and otherwise continue the tensor norm program.
On Certain Stable Wedge Summands of B(𝓩/p)n+
Authors: Harris John C. 
Published: December 2010

AbstractCampbell and Selick have given a natural decomposition of the cohomology of an elementary abelian p-group over the Steenrod algebra. We study the corresponding stable wedge summands of the classifying space B(𝓩/p)n+using representation theory and explicit idempotents in the group ring 𝓕p[GLn(𝓩/p)].
Sequence Entropy and Mild Mixing
Authors: Zhang Qing 
Published: December 2010

Entropy characterizations of different spectral and mixing properties of dynamical systems were dealt with by a number of authors (see [5], [6] and [8]).Given an infinite subset Γ = {tn}of N and a dynamical system (X, β,μ, T) one can define sequence entropy along for any finite Petition ξ, and hΓ(T) —supξ hΓ(T,ξ). In [6] Kushnirenko used sequence entropy to give a characterization of systems with discrete spectrum.
On the Degree of an Analytic Map Germ
Authors: Duszak Zbigniew 
Published: December 2010

AbstractLet ƒ = (ƒ1,… ,ƒn): (ℝn, 0) → (ℝn, 0) be a real analytic mapping and 0 is isolated in ƒ-1 (0). The aim of this paper is to describe the degree deg0ƒ in terms of parametrizations of irreducible components of the real analytic curve given by the equations ƒ1(x) = ̇̇̇= ƒn-1 (x) = 0 near 0 ∈ ℝn.