The Hypergeometric Approach to Integral Transforms and Convolutions

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 Kontorovich--Lebedev 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 Kontorovich--Lebedev Transform. 16. Convolutions of the General Index Transforms. 17. Applications of the Kontorovich--Lebedev Type Convolutions to Integral Equations. 18. Convolutional Ring Calpha. 19. The Fields of the Convolution Quotients. 20. The Cauchy Problem for Erdelyi--Kober Operators. 21. Operational Method of Solution of Some Convolution Equations. References. Author Index. Subject Index. Notations.