Prudnikov / Skórnik Operational Calculus and Related Topics

Erscheinungsjahr 2010
ISBN: 978-1-4200-1149-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 424 Seiten

Reihe: Analytical Methods and Special Functions

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 examines both the analytical and algebraic aspects of operational calculus and includes a comprehensive survey of classical results while stressing new developments in the field. Among the historical methods considered are Oliver Heaviside’s algebraic operational calculus and Paul Dirac’s delta function. Other discussions deal with the conditions for the existence of integral transforms, Jan Mikusinski’s theory of convolution quotients, operator functions, and the sequential approach to the theory of generalized functions. Benefits… · Discusses theory and applications of integral transforms · Gives inversion, complex-inversion, and Dirac’s delta distribution formulas, among others · Offers a short survey of actual results of finite integral transforms, in particular convolution theorems Because Operational Calculus and Related Topics provides examples and illustrates the applications to various disciplines, it is an ideal reference for mathematicians, physicists, scientists, engineers, and students.

Zielgruppe

Mathematicians, physicists, engineers, and students.

Autoren/Hrsg.

Prudnikov, A. P.

Skórnik, K.A.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

INTEGRAL TRANSFORMS

Introduction to Operational Calculus

Integral Transforms — Introductory Remarks

The Fourier Transform

The Laplace Transform

The Mellin Transform

The Stieltjes Transform

The Hilbert Transform

Bessel Transforms

The Mehler–Fock Transform

Finite Integral Transforms

OPERATIONAL CALCULUS

Introduction

The Theorem of Titchmarsh

Operators

Bases of the Operator Analysis

Operators Reducible to Functions

Application of Operational Calculus

GENERALIZED FUNCTIONS

Introduction

Generalized Functions — Functional Approach

Generalized Functions — Sequential Approach

Delta Sequences

Convergent Sequences

Local Properties

Irregular Operations

Hilbert Transform and Multiplication Forms