Год выпуска: 2010 Автор: Sergey Ludkovsky Издательство: LAP Lambert Academic Publishing Страниц: 336 ISBN: 9783843383264
Описание
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 theory of meromorphic functions of the Cayley-Dickson variables is presented. Their properties and methods of calculations of their residues and arguments are described. The third chapter exposes material about differential equations over the Cayley-Dickson algebras. In chapter IV the technique for integration of partial differential equations with variable piecewise continuous or...
