A survey on sampling theory (Q2706518)

Shannon's sampling theory has been developed and extended in several directions. In this paper we give a survey on Shannon's sampling theorem for spaces of generalized functions. First we introduce the Shannon-Kotel'nikov formula, which is the basic theorem of sampling theory, and the sampling theorems for Paley-Wiener space and Bernstein space. Next, we mention the sampling theorem for the space of Fourier transforms of distributions with compact support, i.e. the entire functions with polynomial growth on the real line. Finally, we deal with our new result, a sampling theorem for the entire functions with exponential growth on the real line, its applications, and error estimate.