Analysis over Cayley-Dickson numbers and its applications : Hypercomplex holomorphic functions, meromorphic functions, partial differential equations, operational calculus

Publisher

LAP LAMBERT Academic Publishing

Publication Date

2010

Language

English

ISBN 10

384338326X

ISBN 13

9783843383264

Binding

Soft cover

Condition

Hervorragend

Seller catalogs

B�cher

About this title

Synopsis

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 generalized coefficients is written. The fifth chapter contains results on the non- commutative multidimensional Laplace transforms.

About the Author

LUDKOVSKY SERGEY VICTOR was born on the 08-th of January 1960 in Moscow, Russia, had graduated Department of Mathematics of the Moscow State University (M.V. Lomonosov), had received the Ph. Dr. degree in November 1987, Professor at Department of Applied Mathematics of the Moscow State Technical University MIREA.

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