Carleman’s Formulas in Complex Analysis

This monograph gives a systematic presentation of the Carleman formulas. These enable values of functions holomorphic to a domain to be recovered from their values over a part of the boundary of the domain. Various generalizations of these formulas are considered. Applications are considered to problems of analytic continuation in the theory of functions, and, in a broader context, to problems arising in theoretical and mathematical physics, and to the extrapolation and interpolation of signals having a finite Fourier spectrum. The volume also contains a review of recent results, including those obtained by computer simulation on the elimination of noise in a given frequency band. It is suitable for mathematicians and theoretical physicists whose work involves complex analysis, and those interested in signal processing.