Analysis over Cayley-Dickson numbers and its applications
Sergey Ludkovsky
Broschiertes Buch

Analysis over Cayley-Dickson numbers and its applications

Hypercomplex holomorphic functions, meromorphic functions, partial differential equations, operational calculus

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The book is devoted to non-commutative analysis over Cayley-Dickson algebras and its applications to partial differential equations. In the first chapter super-differentiability of functions is described on regions of the real Cayley-Dickson algebra. The non-commutative analog of the Cauchy integral as well as criteria for functions of a Cayley-Dickson variable to be analytic are exposed. Among the main results we have the Cayley- Dickson algebras analogs of Caychy's theorem, Hurtwitz', argument principle, Mittag-Leffler's, Rouche's and Weierstrass' theorems, etc. In the second chapter the the...