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Representations of Sheffer Polynomials
Author(s) -
Di Bucchianico A.
Publication year - 1994
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm19949311
Subject(s) - mathematics , corollary , mathematical proof , algebra over a field , convolution (computer science) , representation (politics) , pure mathematics , invariant (physics) , computer science , artificial intelligence , geometry , politics , artificial neural network , political science , law , mathematical physics
In this paper we investigate which Sheffer polynomials can be represented as moments of convolution semigroups of probability measures. We also obtain general integral representations for shift‐invariant operators and for umbral operators. As a corollary, we obtain new proofs for representation theorems for Sheffer polynomials due to Sheffer and Thorne.