Umbral Calculus and Cancellative Semigroup Algebras
Abstract
Description
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of cancellative semigroup, their convolution algebras, and tokens between them provides a common language for description of objects from these three fields.
Keywords: cancellative semigroups, umbral calculus, harmonic analysis, token, convolution algebra, integral transform
LaTeX, 32 pages, paper is completely revised from the title to bibliography
LaTeX, 32 pages, paper is completely revised from the title to bibliography