1. Functions of several Cayley-Dickson variables and manifolds over them.
- Author
-
Ludkovsky, S.
- Subjects
- *
CAYLEY algebras , *COPYING , *ALGEBRAIC number theory , *INTEGRAL representations , *MANIFOLDS (Mathematics) , *MATHEMATICAL analysis - Abstract
Functions of several octonion variables are investigated and integral representation theorems for them are proved. By using these theorems, solutions of $$\tilde \partial - equations$$ are studied. More generally, functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, and Koppelman type used in complex analysis are proved in a new generalized form for functions of Cayley-Dickson variables instead of complex variables. Moreover, analogues of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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