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
V.V. Kisil, Umbral Calculus and Cancellative Semigroup Algebras. Z. Anal. Anwend. 19 (2000), no. 2 pp. 315–338