Bücher der Reihe Analytical Methods and Special Functions

Based on the Sobolev-Schwartz concept of Generalized Functions, this text presents general theory including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner, Poisson integraltransforms and operational calculus. The theory of Fourier series, abelian theorems, boundary values of helomorphic functions for one and several variables is covered.

This volume presents a comprehensive treatment of hypersingular integrals and their applications. Hypersingular integrals arise as constructions inverse to potential type operators and are realised by these approaches: method of regularization; method of finite differences.

Gives an introduction to operational calculus, integral transforms, and generalized functions, the backbones of pure and applied mathematics. This text examines both the analytical and algebraic aspects of operational calculus and includes a comprehensive survey of classical results while stressing fresh developments in the field.