Transformations, Transmutations, and Kernel Functions

Transformations, Transmutations, and Kernel Functions PDF

Author: H Begehr

Publisher: CRC Press

Published: 1993-09-23

Total Pages: 286

ISBN-13: 9780582091092

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Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.

The Kernel Function and Conformal Mapping

The Kernel Function and Conformal Mapping PDF

Author: Stefan Bergman

Publisher: American Mathematical Soc.

Published: 1950-03

Total Pages: 269

ISBN-13: 0821815059

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The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of ""The Kernel Function"". The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.

Transformations, Transmutations, and Kernel Functions, Volume I

Transformations, Transmutations, and Kernel Functions, Volume I PDF

Author: Heinrich G. W. Begehr

Publisher: Chapman and Hall/CRC

Published: 1992-12-14

Total Pages: 424

ISBN-13:

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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.

Kernel Determination Problems in Hyperbolic Integro-Differential Equations

Kernel Determination Problems in Hyperbolic Integro-Differential Equations PDF

Author: Durdimurod K. Durdiev

Publisher: Springer Nature

Published: 2023-06-18

Total Pages: 390

ISBN-13: 9819922607

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This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional “impacts” or “explosions”. This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.