Functions of several Cayley-Dickson variables and manifolds over them

Details Functions of several Cayley-Dickson variables and manifolds over them Functions of several Cayley-Dickson variables and manifolds over them

2006-03-13

arxiv.org/abs/math/0603301v1

J. Mathem. Sci. 2007

Mathematics

Complex Variables

Scientific paper

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are proved in the new generalized form for functions of Cayley-Dickson variables instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson graded algebras are defined and investigated.

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