ABSTRACT
Orthogonal series play an important part in many areas of mathematics as well as in applications. They constitute an easy way of representing a function in terms of a series and may replace complicated operators on the function by simpler ones on the coefficients of the series. The most familiar orthogonal systems are the trigonometric and the various orthogonal polynomials. Not so familiar but becoming increasingly widely used are the Haar, the Shannon, and wavelet systems.
