In this approachable introduction to the topic, Distribution, Integral Transforms and Applications makes clear the theory of distributions and integral transforms, exploring the general theory, examples and applications. The authors emphasize the remarkable connection between distribution theory and the classical theory and analysis of differential equations. First they explain the theory of the Lebesque integral as a fundamental tool in the proofs of many theorems. They also give practical hints on using the theory of distributions when classical analysis is insufficient. The text is...

Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will...

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.

Along with more than 2100 integral equations and their solutions, this handbook outlines exact analytical methods for solving linear and nonlinear integral equations and provides an evaluation of approximate methods. Each section provides examples that show how methods can be applied to specific equations.

Even though the theories of operational calculus and integral transforms are centuries old, these topics are constantly developing, due to their use in the fields of mathematics, physics, and electrical and radio engineering. Operational Calculus and Related Topics highlights the classical methods and applications as well as the recent advances in the field.

Combining the best features of a textbook and a monograph, this volume presents an introduction to operational calculus, integral transforms, and generalized functions, the backbones of pure and applied mathematics. The text...

Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.

Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spectrum is arbitrary. The Weyl matrix is introduced and studied as a spectral characteristic. The second part of the book is devoted to solving incomplete inverse problems when a priori information about the operator or its spectrum is available and...