Distributions and Analytic Functions: 206 (Pitman Research Notes in Mathematics Series) - Softcover

Carmichael, R.D.; Mitrovic, Dragisa

Softcover

ISBN 10: 0582018560 ISBN 13: 9780582018563

Publisher: Longman Higher Education, 1989

Synopsis

The authors present a survey of distributions and complex variables and give detailed proofs and examples of their analysis. Areas which are examined include the representation of distributions as boundary values of analytic functions in one and several variables; the development of the one-dimensional boundary value analysis and the application of results from the one-dimensional distributional boundary value to produce solutions to boundary value problems and convolution equations.
Readership: Professional mathematicians and graduate research students involved in functional analysis, complex variables and harmonic analysis. The book will also be of interest to physicists working in quantum field theory and engineers.

About this title

Synopsis

Analysis concerning the representation of distributions in the sense of L.Schwartz as boundary values of analytic functions in one and several variables is presented in this book. The contents review the facts concerning distributions and several complex variables and give detailed proofs of the analysis. Except for one section concerning vector valued distributions, the book concerns the scalar valued distributions as originally introduced by L.Schwartz. Of particular interest throughout the development of one-dimensional boundary analysis is the construction and application of the distributional Plemelj relations. Throughout the book examples of the topics which are discussed are given and the one-dimensional distributional boundary value results are applied to yield solutions to distributional generalizations of boundary value problems of Plemlj, Hilbert, Reimann-Hilbert and Dirichlet and to convolution equations. The text is aimed at mathematical physicists and engineers as well as mathematicians.

Edition details

• Publisher: Longman Higher Education
• Publication date: 1989
• Language: English
• ISBN 10: 0582018560
• ISBN 13: 9780582018563
• Binding: Paperback
• Number of pages: 368