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 semigroups, their convolution algebras, and between them provides a common language for description of objects from these three fields.
Cite this article
Vladimir V. Kisil, Umbral Calculus and Cancellative Semigroup Algebras. Z. Anal. Anwend. 19 (2000), no. 2, pp. 315–338DOI 10.4171/ZAA/953