SLICE MONOGENIC FUNCTIONS OF A CLIFFORD VARIABLE VIA THE S-FUNCTIONAL CALCULUS

Fabrizio Colombo; David P. Kimsey; Stefano Pinton; Irene Sabadini

doi:10.1090/bproc/94

SLICE MONOGENIC FUNCTIONS OF A CLIFFORD VARIABLE VIA THE S-FUNCTIONAL CALCULUS

Fabrizio Colombo, David P. Kimsey, Stefano Pinton, Irene Sabadini

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S-functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of suﬃciently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any diﬃculty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra R_n. The methodology can be generalized, for example, to handle the case of noncom-muting matrix variables.

Original language	English
Pages (from-to)	281-296
Number of pages	16
Journal	Proceedings of the American Mathematical Society, Series B
Volume	8
DOIs	https://doi.org/10.1090/bproc/94
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

S-functional calculus
S-spectrum
Slice monogenic functions
noncommuting matrix variables

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Discrete Mathematics and Combinatorics

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title = "SLICE MONOGENIC FUNCTIONS OF A CLIFFORD VARIABLE VIA THE S-FUNCTIONAL CALCULUS",

abstract = "In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S-functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of suﬃciently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any diﬃculty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra Rn. The methodology can be generalized, for example, to handle the case of noncom-muting matrix variables.",

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AU - Sabadini, Irene

PY - 2021/1/1

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N2 - In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S-functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of suﬃciently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any diﬃculty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra Rn. The methodology can be generalized, for example, to handle the case of noncom-muting matrix variables.

AB - In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S-functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of suﬃciently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any diﬃculty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra Rn. The methodology can be generalized, for example, to handle the case of noncom-muting matrix variables.

KW - S-functional calculus

KW - S-spectrum

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KW - noncommuting matrix variables

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SLICE MONOGENIC FUNCTIONS OF A CLIFFORD VARIABLE VIA THE S-FUNCTIONAL CALCULUS

Abstract

Keywords

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