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 -