Fourier Approximation In Lp-Spaces: A Summability Approach

The subject of Fourier Approximation has received special attention during the last few decades due to its wide applications in the field of Physics, Aeronautics, Signal Analysis in general & designing of digital filters with Finite Impulse Response in particular. Functions (signals) belonging to Lp- spaces are assumed to be the most appropriate signals for the practical purposes, for example L1, L2 and L? are particularly interesting spaces for Engineers. Fourier approximation in Lip(p ? 1)- spaces using summability techniques is a field of paramount importance. In Fourier analysis, since Fourier coefficients are computable and applicable, researchers have already established many classical and interesting results by assuming monotonicity on the coefficients. One of the important and natural ways to improve these results is to loose the restriction on monotonicity conditions. Under this background many generalizations of monotonicity conditions were suggested. This book is an attempt in the direction of improving the present status of the subject.