If f: R R belongs to C(R) and f(j) is periodic for all j > 0, prove

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If f: R †’ R belongs to Cˆž(R) and f(j) is periodic for all j > 0, prove that Sf is term-by-term differentiable on R. In fact, show that

uniformly for all j ˆˆ N.

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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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If f: R R belongs to C(R) and f(j) is periodic for all j > 0, prove

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di f dxi (x) =-dx) (ak(f) cos kx + bk(f) sin kx) に!

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Fix j N Since It follows from Theorem 1423 that d j dx j a k f cos kx 1k 2 for k ...View the full answer

An Introduction to Analysis

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