Slice regular functions in several variables

In this paper, we lay the foundations of the theory of slice regular functions in several (non-commuting) variables ranging in any real alternative ∗ -algebra, including quaternions, octonions and Clifford algebras. This higher dimensional function theory is an extension of the classical theory of h...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Mathematische Zeitschrift Ročník 302; číslo 1; s. 295 - 351
Hlavní autoři: Ghiloni, Riccardo, Perotti, Alessandro
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022
Springer Nature B.V
Témata:
Algebra
Analytic functions
Complex variables
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
Power series
Quaternions
Real variables
Series expansion
Slice regular functions
Cauchy integral formula
Quaternions
Octonions
Real alternative algebras
30G35
32A30
Functions of hypercomplex variables
Clifford algebras
17D05
ISSN:0025-5874, 1432-1823
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:In this paper, we lay the foundations of the theory of slice regular functions in several (non-commuting) variables ranging in any real alternative ∗ -algebra, including quaternions, octonions and Clifford algebras. This higher dimensional function theory is an extension of the classical theory of holomorphic functions of several complex variables. It is based on the construction of a family of commuting complex structures on R 2 n . One of the relevant aspects of the theory is the validity of a Cauchy-type integral formula and the existence of ordered power series expansions. The theory includes all polynomials and power series with ordered variables and right coefficients in the algebra. We study the real dimension of the zero set of polynomials in the quaternionic and octonionic cases and give some results about the zero set of polynomials with Clifford coefficients. In particular, we show that a nonconstant polynomial always has a non empty zero set.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-022-03066-9