2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148821We 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 transformLaTeX, 32 pages, paper is completely revised from the title to bibliographyFunctional Analysis43A20; 05A40, 20N++text