Umbral Calculus and Cancellative Semigroup Algebras
Vladimir V. Kisil (Univ. of Leeds)
TL;DR
This paper explores the connections between umbral calculus, harmonic analysis, and functional analysis through the framework of cancellative semigroup convolution algebras, providing a unified language for these mathematical fields.
Contribution
It introduces a systematic approach using cancellative semigroups and tokens to unify concepts across combinatorics, functional analysis, and harmonic analysis.
Findings
Established links between umbral calculus and harmonic analysis.
Developed a framework using convolution algebras of cancellative semigroups.
Provided new tools for describing objects across the three mathematical fields.
Abstract
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
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Advanced Topics in Algebra · Advanced Algebra and Logic