Two-dimensional problem of two Coulomb centers at small intercenter distances

We use analytic methods to analyze the discrete spectrum for the problem (Z₁eZ₂)₂ in the united-atom limit (R ≪ 1) and obtain asymptotic expansions for the quantum defect and energy terms of the system (Z₁eZ₂)₂ at small intercenter distances R up to terms of the order O(R⁶). We investigate the effect of the dimensionality factor on the energy spectrum of the hydrogen molecular ion H ₂ ⁺ . __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 269–287, August, 2006.     

Bessel capacities and rectangular differentiation in Besov spaces

We consider the differentiation of integrals of functions in Besov spaces with respect to the basis of arbitrarily oriented rectangular parallelepipeds in Rn. We study almost everywhere convergence with respect to Bessel capacities. These outer measures are more sensitive than n-dimensional Lebesgue measure, and therefore we improve the positive results in [H. Aimar, L. Forzani, V. Naibo, Rectangular differentiation of integrals of Besov functions, Math. Res. Lett. 9 (2-3) (2002) 173-189].     

A characterization of generalized poles of generalized Nevanlinna functions

Generalized poles of a generalized Nevanlinna function Q ∈ ??_κ (??) are defined in terms of the operator representation of Q . In this paper those generalized poles that are not of positive type and their degrees of non‐positivity are characterized analytically by means of pole cancellation functions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains

We consider the Dirichlet eigenvalue problem for the Laplace operator on a variable nonsmooth domain. We extend a result of Lupo and Micheletti concerning the structure of the set of domain perturbations which leave the multiplicity of an eigenvalue unchanged, and we study the set of perturbations which leave a certain eigenvalue unchanged.     

On classes of analytic functions defined by convolution with incomplete beta functions

Carlson and Shaffer [SIAM J. Math. Anal. 15 (1984) 737-745] defined a convolution operator L(a,c) on the class A of analytic functions involving an incomplete beta function ?(a,c;z) as L(a,c)f=?(a,c)?f. We use this operator to introduce certain classes of analytic functions in the unit disk and study their properties including some inclusion results, coefficient and radius problems. It is shown that these classes are closed under convolution with convex functions.     

The Fractional Derivatives of a Fractal Function

The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Weierstrass function.     

解析Dirichlet级数的准确零(R)级

本文研究了右半平面内解析Dilrichlet级数的准确零(R)级,减弱了已有结果的条件,得到了更强的结论并简化了原证明．     

LU factorizations, q = 0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q = 0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas. Dedicated to Dick Askey on the occasion of his seventieth birthday. 2000 Mathematics Subject Classification Primary—33D45, 33D80 Work done at KdV Institute, Amsterdam and supported by NWO, project number 613.006.573.     

On a Measure of Non-compactness for Some Classical Operators

The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified.