List questions from fourier-analysis

Published on 12 Apr 2026 - 0:19

140

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What does $\langle f,g \rangle:=\frac{2}{T}\int f(x)g(x)dx, T>0$ mean?

Published on 10 May 2026 - 14:44

1.6k

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Retrieving function from Fourier coefficients $c_n=1/n$

Published on 10 May 2026 - 14:41

88

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For any $f\in L^1(S^1)$ and let $y\in\mathbb{R}$, let $f_y$ be defined as $f_y(x)=f(x+y)$. Prove that $\lim_{y\to 0 } ||f_y-f||=0.$

Published on 13 May 2026 - 18:53

246

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Parseval's theorem and $L_2$ space

Published on 10 May 2026 - 22:53

671

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Intuition about Dirichlet Kernel

Published on 14 May 2026 - 3:54

115

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Showing $\widehat{f \star g}(\xi) = \widehat{f}(\xi) \widehat{g}(\xi)$

Published on 13 May 2026 - 18:53

512

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boundness about Fejer kernel

Published on 10 May 2026 - 14:40

238

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May someone of you provide me (if possible) an expression for the F.T. of $\tan(x)$?

Published on 05 May 2026 - 16:56

156

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Convolution interchangeable with multiplication on white noise?

Published on 11 May 2026 - 1:01

979

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Fourier transform of meromorphic function

Published on 10 May 2026 - 14:11

57

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formula for Walsh-Fourier series

Published on 11 Apr 2026 - 8:47

212

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How to calculate $\int\limits_{-\pi}^{\pi}f(x)\cos^5(nx)\,dx$ using Fourier series?

Published on 10 May 2026 - 16:36

373

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Squared Dirichlet integral.

Published on 10 May 2026 - 14:40

68

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An equality in Fourier analysis

Published on 10 May 2026 - 15:44

List Question

convolution chi function with itself

What does $\langle f,g \rangle:=\frac{2}{T}\int f(x)g(x)dx, T>0$ mean?

Retrieving function from Fourier coefficients $c_n=1/n$

For any $f\in L^1(S^1)$ and let $y\in\mathbb{R}$, let $f_y$ be defined as $f_y(x)=f(x+y)$. Prove that $\lim_{y\to 0 } ||f_y-f||=0.$

Parseval's theorem and $L_2$ space

Intuition about Dirichlet Kernel

Showing $\widehat{f \star g}(\xi) = \widehat{f}(\xi) \widehat{g}(\xi)$

boundness about Fejer kernel

May someone of you provide me (if possible) an expression for the F.T. of $\tan(x)$?

Convolution interchangeable with multiplication on white noise?

Fourier transform of meromorphic function

formula for Walsh-Fourier series

How to calculate $\int\limits_{-\pi}^{\pi}f(x)\cos^5(nx)\,dx$ using Fourier series?

Squared Dirichlet integral.

An equality in Fourier analysis

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