Introduction to fourier series - Lasser, Rupert (Monographs and textbooks in pure and applied mathematics, 1996)
"This concise, self-contained reference/text addresses all of the major topics in Fourier series - emphasizing the concept of approximate identities; presenting applications, particularly in time series analysis; stressing throughout the idea of homogeneous Banach spaces; and providing new results." "Utilizing techniques from functional analysis and measure theory, Introduction to Fourier Series furnishes representation theorems such as Herglotz's theorem and Wiener's theorem...compares the performance of approximate identities with elements of best approximation...develops results on spectral synthesis applying Banach algebra techniques...derives characterizations of absolute convergence of Fourier series...studies Fourier and Plancherel transformations on the real axis establishing the relation to Fourier series using the Poisson summation formula...and more." "Written by an internationally recognized expert, Introduction to Fourier Series is an incomparable reference for pure and applied mathematicians and signal processing engineers and the text of choice for all upper-level undergraduate and graduate students taking courses in Fourier analysis, harmonic analysis, or approximation theory with a basic knowledge of real and abstract analysis."--BOOK JACKET.