Continuous Sheffer families I

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Campos-Orozco, J. S.¹  Gale, J. E.^2,3 

[1] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City 09340, DF, Mexico

[2] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

[3] Univ Zaragoza, IUMA, E-50009 Zaragoza, Spain

关键词: Convolution semigroup;    Locally convex algebra;    Special function;    Mellin transform;    Gamma function;    Sheffer family;   

DOI  :  10.1016/j.jmaa.2013.04.005

来源: Elsevier

【 摘 要 】

A convolution locally convex algebra U of holomorphic functions is introduced as a natural setting where to place special functions, which are continuously indexed counterparts to sequences of the classical orthogonal polynomials arising in the umbral calculus. In this way, such functions become semigroups, or Sheffer-type classes associated with semigroups, in the algebra U. A central role in this approach is to be played by the Gamma function. We also discuss the Hermite and Lerch functions to illustrate the theory. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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