The Hypergeometric Approach to Integral Transforms and Convolutions / Edition 1by S.B. Yakubovich, Yury Luchko
Pub. Date: 05/31/1994
Publisher: Springer Netherlands
This volume deals with the theory and applications of integral transforms and convolutions of certain classes of integral, integrodifferential equations, and operational calculus. An extensive discussion is presented, based on the universal hypergeometric approach, i.e. many constructions of convolution and integral transforms are obtained using the theory of
This volume deals with the theory and applications of integral transforms and convolutions of certain classes of integral, integrodifferential equations, and operational calculus. An extensive discussion is presented, based on the universal hypergeometric approach, i.e. many constructions of convolution and integral transforms are obtained using the theory of MellinBarnes integrals and the Mellin transforms of hypergeometric type functions. This approach is spread on so-called index transforms, in which the KontorovichLebedev and the MehlerFock transforms play a very important part. The general constructions of index transforms are given and application to the evaluation of improper integral with respect to a parameter of special function (index) is considered. The operational calculus for general integrodifferential operators is constructed for both new types of convolutions. The book is self-contained, and includes a list of symbols with definitions, author and subject indices, and an up-to-date bibliography.
This work will be of interest to researchers and graduate students in the mathematical and physical sciences whose work involves integral transforms and convolutions.
Table of Contents
Preface. 1. Preliminaries. 2. Mellin Convolution Type Transforms with Arbitrary Kernels. 3. H- and G-Transforms. 4. The Generalized H- and G-Transforms. 5. The Generating Operators of Generalized H-Transforms. 6. The KontorovichLebedev Transform. 7. General W-Transform and its Particular Cases. 8. Composition Theorems of Plancherel Type for Index Transforms. 9. Some Examples of Index Transforms and their New Properties. 10. Applications to Evaluation of Index Integrals. 11. Convolutions of Generalized H-Transforms. 12. Generalization of the Notion of Convolution. 13. Leibniz Rules and their Integral Analogues. 14. Convolutions of Generating Operators. 15. Convolution of the KontorovichLebedev Transform. 16. Convolutions of the General Index Transforms. 17. Applications of the KontorovichLebedev Type Convolutions to Integral Equations. 18. Convolutional Ring Calpha. 19. The Fields of the Convolution Quotients. 20. The Cauchy Problem for ErdelyiKober Operators. 21. Operational Method of Solution of Some Convolution Equations. References. Author Index. Subject Index. Notations.
and post it to your social network
Most Helpful Customer Reviews
See all customer reviews >