TY - JOUR

T1 - POLY SLICE MONOGENIC FUNCTIONS, CAUCHY FORMULAS AND THE PS-FUNCTIONAL CALCULUS

AU - Alpay, Daniel

AU - Colombo, Fabrizio

AU - Diki, Kamal

AU - Sabadini, Irene

N1 - Funding Information:
Acknowledgements. Daniel Alpay thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported this research.
Publisher Copyright:
© Copyright by THETA, 2020

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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.

AB - 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.

KW - Cauchy formulas

KW - Modified s-resolvent operators

KW - Poly slice monogenic function

KW - Ps-resolvent operators

KW - Spectral theory on the s-spectrum

UR - http://www.scopus.com/inward/record.url?scp=85141744246&partnerID=8YFLogxK

U2 - 10.7900/jot.2021feb20.2347

DO - 10.7900/jot.2021feb20.2347

M3 - Article

AN - SCOPUS:85141744246

SN - 0379-4024

VL - 88

SP - 309

EP - 364

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -