List questions from fourier-analysis

Published on 08 Feb 2018 - 23:19

137

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

Published on 25 Mar 2026 - 7:46

1.6k

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

Published on 25 Mar 2026 - 4:36

85

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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 28 Mar 2026 - 13:42

240

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Parseval's theorem and $L_2$ space

Published on 23 Mar 2026 - 4:03

665

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Intuition about Dirichlet Kernel

Published on 27 Mar 2026 - 9:47

112

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

Published on 29 Mar 2026 - 5:43

508

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boundness about Fejer kernel

Published on 25 Mar 2026 - 7:38

230

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

Published on 19 Mar 2026 - 16:27

153

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Convolution interchangeable with multiplication on white noise?

Published on 26 Mar 2026 - 3:00

970

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Fourier transform of meromorphic function

Published on 22 Mar 2026 - 9:24

54

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formula for Walsh-Fourier series

Published on 28 Mar 2026 - 10:16

209

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

Published on 25 Mar 2026 - 4:41

369

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Squared Dirichlet integral.

Published on 25 Mar 2026 - 2:56

65

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An equality in Fourier analysis

Published on 27 Mar 2026 - 7:26

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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