2020/11/27 by Daniel Alpay, Alpay, Daniel, Fabrizio Colombo +5 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic and Geometric Analysis #Applied mathematics #Calculus (dental) #Cauchy distribution #Fractional calculus #Functional calculus #Geometry #Mathematical analysis #Mathematics #Mathematics and Applications #Physics #Product (mathematics) #Pure mathematics #Quantum mechanics #Spectral theory #Spectrum (functional analysis) #math.FA
paper · pdf · doi:10.48550/arxiv.2011.13912
Accepted, to appear in J. Oper. Theory
openalex publication_date 2020/11/27 · arxiv created 2021/11/12 · arxiv updated 2021/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the S-spectrum has applications, for example, in the formulation of quaternionic quantum mechanics, in Schur analysis and in fractional diffusion problems. In this paper we introduce and study the theory of poly slice monogenic functions, also proving some Cauchy type integral formulas. Then we introduce the associated functional calculus, called PS-functional calculus, which is the polyanalytic version of the S-functional calculus and which is based on the notion of S-spectrum. We study some different formulations of the calculus and we prove some of its properties, among which the product rules.