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Analysis over CayleyDickson numbers and its applications: Hypercomplex holomorphic functions, meromorphic functions, partial di,Used
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The book is devoted to noncommutative analysis over CayleyDickson algebras and its applications to partial differential equations. In the first chapter superdifferentiability of functions is described on regions of the real CayleyDickson algebra. The noncommutative analog of the Cauchy integral as well as criteria for functions of a CayleyDickson variable to be analytic are exposed. Among the main results we have the Cayley Dickson algebras analogs of Caychy's theorem, Hurtwitz', argument principle, MittagLeffler's, Rouche's and Weierstrass' theorems, etc. In the second chapter the theory of meromorphic functions of the CayleyDickson 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 CayleyDickson 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.
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