On the generators of Clifford semigroups: Polynomial resolvents and their integral transforms

This paper deals with generators A of strongly continuous right linear semigroups in Banach two-sided spaces whose set of scalars is an arbitrary Clifford algebra Cℓ(0,n). We study the invertibility of operators of the form P(A), where P(x)∈R[x] is any real polynomial, and we give an integral repres...

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Vydané v:Journal of mathematical analysis and applications Ročník 521; číslo 1; s. 126905
Hlavní autori: Ghiloni, Riccardo, Recupero, Vincenzo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.05.2023
Predmet:
Clifford algebras
Functional calculus
Functions of hypercomplex variables
Laplace transform
Quaternions
Slice regular semigroups
Clifford algebras
Functions of hypercomplex variables
Quaternions
Laplace transform
Slice regular semigroups
Functional calculus
ISSN:0022-247X, 1096-0813
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Popis
Shrnutí:This paper deals with generators A of strongly continuous right linear semigroups in Banach two-sided spaces whose set of scalars is an arbitrary Clifford algebra Cℓ(0,n). We study the invertibility of operators of the form P(A), where P(x)∈R[x] is any real polynomial, and we give an integral representation for P(A)−1 by means of a Laplace-type transform of the semigroup T(t) generated by A. In particular, we deduce a new integral representation for the spherical quadratic resolvent of A (also called pseudoresolvent of A). As an immediate consequence, we also obtain a new proof of the well-known integral representation for the spherical resolvent of A.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126905