Suppose that f: R R is periodic, piecewise continuous, and of bounded variation on R. Prove

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Suppose that f: R → R is periodic, piecewise continuous, and of bounded variation on R. Prove that if S is a trigonometric series which converges to (f(x+) + f(x-))/2 for all x ∈ R, then S is the Fourier series of f.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:30 AM

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Suppose that f: R R is periodic, piecewise continuous, and of bounded variation on R. Prove

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Let gx fx fx2 for each x R By Theorem 1429 ...View the full answer

An Introduction to Analysis

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