An Introduction to Fourier Analysis and Generalised Functions

This monograph on generalised functions Fourier integrals and Fourier series is intended for readers who while accepting that a theory where each point is proved is better than one based on conjecture nevertheless seek a treatment as elementary and free from complications as possible. Little detailed knowledge of particular mathematical techniques is required; the book is suitable for advanced university students and can be used as the basis of a short undergraduate lecture course. A valuable and original feature of the book is the use of generalised-function theory to derive a simple widely applicable method of obtaining asymptotic expressions for Fourier transforms and Fourier coefficients.