Distributions Theory & Applications

be a function on the line that equals 0 away from 0 and is in?nite at 0 in such a way that its total integral is 1. x/ is an object that one frequently would like to use, but of course there is no such function, because a function that is 0 everywhere except at one point has integral 0.

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework.