Böcker i Analytical Methods and Special Functions-serien

An approachable introduction to the theory of distributions and integral transforms, the text emphasizes the remarkable connections of distribution theory with the classical analysis and the theory of differential equations.

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.

Integral transforms, operational calculus, and generalized functions are the backbone of many branches of pure and applied mathematics. Combining the best features of a textbook and a monograph, Operational Calculus and Related Topics provides an introduction to these subjects. The book includes a comprehensive survey of classical results and highlights recent advances in the field. Including applications to various disciplines, this text considers both the analytical as well as the algebraic aspects of operational calculus, making it ideal for mathematicians, physicists, students, scientists, and engineers applying such mathematical methods and performing research in a wide range of areas.

The focus of this text is on the behaviour of Fourier transforms in the region of analyticity and the distribution of their zeros. Three classes of Fourier transforms are examined: Fourier (Laplace) transforms on the halfline, Fourier transforms of measures with compact support and Fourier transforms of rapidly decreasing functions (on whole line).

Consisting of two parts, this text presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spectrum is arbitrary, then solves incomplete inverse problems when a priori information about the operator or its spectrum is available and these problems are significant in applications.

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.

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.