Transformations, Transmutations, and Kernel Functions, Volume I (Monographs and Surveys in Pure and Applied Mathematics) - Tapa dura

Begehr, H; Gilbert, Robert P.

9780582026957: Transformations, Transmutations, and Kernel Functions, Volume I (Monographs and Surveys in Pure and Applied Mathematics)

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ISBN 10: 0582026954 ISBN 13: 9780582026957

Editorial: Chapman and Hall/CRC, 1992

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A broad ranging collection of recent results in the subject covering areas from plane elasticity to second and higher order elliptic equations. The chapters may be read individually, providing a more accessible forum for the applications.

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Complex analytic methods are a powerful tool for special partial differential equations and systems. In order to make these methods applicable for a wider class one uses transformations and transmutations. Transformations in this sense appear e.g. in the integral operator methods of Bergman and Vekua. Transmutations as were introduced by R.Carroll are intertwinings of operators which transport structure between the theories of the involved operators as e.g. properties of solutions to related equations. Transmutations occasionally are achieved via kernel functions, another important concept in the theory of function theoretic methods. This monography collects recent results a lot of which the authors were involved with. They range from plane elasticity to second and higher order elliptic equations and to evolutionary equations, from boundary value problems to moving boundary problems. From elliptic systems to systems of composite type and to pseudoparabolic systems, from generalized analytic to generalized hyperanalytic functions and to Clifford analysis.

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