(Fourier series) (a) Show that the pointwise convergent series sin(nx) n1/2 1n=1 cannot converge uniformly to a square integrable function f in [-T, T). (b) Let f(x) be 2n periodic and piecewise...

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(Fourier series)<br>(a)<br>Show that the pointwise convergent series<br>sin(nx)<br>n1/2<br>1n=1<br>cannot converge uniformly to a square integrable function f in [-T, T).<br>(b)<br>Let f(x) be 2n periodic and piecewise smooth. Prove that its Fourier series converges<br>uniformly and absolutely to f.<br>

Extracted text: (Fourier series) (a) Show that the pointwise convergent series sin(nx) n1/2 1n=1 cannot converge uniformly to a square integrable function f in [-T, T). (b) Let f(x) be 2n periodic and piecewise smooth. Prove that its Fourier series converges uniformly and absolutely to f.

Jun 05, 2022

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(Fourier series) (a) Show that the pointwise convergent series sin(nx) n1/2 1n=1 cannot converge uniformly to a square integrable function f in [-T, T). (b) Let f(x) be 2n periodic and piecewise...

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