Distributions in the Physical and Engineering Sciences, Volume 1

Alexander I. Saichev was Professor of Mathematics at the Radio Physics Faculty of the Nizhny Novgorod University and a Professor in the Department of Management, Technology, and Economics at the Swiss Federal Institute of Technology. Wojbor A. Woyczynski is Professor of Mathematics and Director of the Center for Stochastic and Chaotic Processes in Science and Technology at Case Western University.

I Distributions and their Basic Applications.- 1 Basic Definitions and Operations.- 2 Basic Applications: Rigorous and Pragmatic.- II Integral Transforms and Divergent Series.- 3 Fourier Transform.- 4 Asymptotics of Fourier Transforms.- 5 Stationary Phase and Related Method.- 6 Singular Integrals and Fractal Calculus.- 7 Uncertainty Principle and Wavelet Transforms.- 8 Summation of Divergent Series and Integrals.- A Answers and Solutions.- A.1 Chapter 1. Definitions and operations.- A.2 Chapter 2. Basic applications.- A.3 Chapter 3. Fourier transform.- A.4 Chapter 4. Asymptotics of Fourier transforms.- A.5 Chapter 5. Stationary phase and related methods.- A.6 Chapter 6. Singular integrals and fractal calculus.- A.7 Chapter 7. Uncertainty principle and wavelet transform.- A. 8 Chapter 8. Summation of divergent series and integrals.- B Bibliographical Notes.