This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses throughout the idea of homogenous Banach spaces and provides recent results. Techniques from functional analysis and measure theory are utilized.;College and university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.
". . .an excellent introduction. . ..warmly recommended to everyone who wants to make a quick acquaintance with Fourier series. "
---Zentralblatt fur Mathematik
Fourier coefficients; approximate identities; approximate identities; approximate identities and pointwise convergence; square integrable functions; convergence of Fourier series in norm; local convergence; characterization of Fourier coefficients; Hilbert transform; approximate identities. Triangular schemes; elements of best approximation; poisson integrals and hardy spaces; conjugation of approximate identities; Szego-Kolmogoriv-theorem; absolute convergence of Fourier series; Fourier transform on R; plancherel transform on R; poisson summation-formula.