PSWF series of slowly growing functions

Band-limited signals of finite energy, i.e., functions in L 2 , form the setting for much of signal processing. However, many signals of practical interest do not have finite energy. In this work we extend some results involving prolate spheroidal wave functions (PSWFs) to such signals. We consider those functions whose Fourier transforms have compact support in the sense of generalized functions and obtain convergence results for their PSWF expansions.