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Book review

Author(s) Srivastava, H.M.
Buschman, R.G.
Title Theory and applications of convolution integral equations
Publisher Kluwer
Year of publication 1992
Reviewed by Günter Vojta

Integral equations of the convolution type are ubiquitous in the fields of mathematical and applied sciences. The possibility to solve them by Fourier, Laplace and Mellin transform methods and generally by operator methods makes these equations very useful in the practice of many branches of physics, systems theory and engineering. Thus, the publication of the book under review is to be highly appreciated. It is a revised and enlarged version of the work Convolution integral equations with special function kernels by the same authors (Wiley/Halsted, 1977). Essentially it represents a state-of-the-art report together with extended inversion tables and an updated full bibliography.

The work starts with an introduction comprising a brief historical review and a classification of the types of integral equations treated. Then six shorter chapters follow containing material on special function kernels, basic theorems, illustrative examples, integral equations of the second and other kinds, convolutions with different intervals of integration, and open questions and direction of further research. Included are such interesting topics as Mikusinski operators, fractional integrals, and certain classes of nonlinear integral equations and integro-differential equations being of special importance in theoretical physics.

A list of symbols (9 pp.) precedes the extensive and well-classified inversion tables (80 pp.). The bibliography (35 pp.) with full titles of all publications is extremely useful. An author index and a subject index (10 pp.) conclude the work.

The very systematic, well-organized and compact representation of the truly broad material certainly renders good service to research workers, teachers and students of many branches of pure and applied sciences. This book is a must for any library and is warmly recommended to all whose work involves the theory and the applications of integral equations.