List questions from fourier-analysis

Published on 14 Apr 2026 - 18:47

428

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Fourier transform of the dilation of a distribution

Published on 10 Apr 2026 - 0:56

36

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$f(t)=\sum_{n=1}^{\infty}2\sin^{3}( \frac{\pi n}{2})\exp(\frac {-n^{2}\pi^{2}t}{2}).$ find $a,b $ such that $f(t)\sim ae^{-bt}$

Published on 16 Apr 2026 - 2:25

35

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Prove that "$\sigma_n(S,t)\ge 0$ for infinitely many $n$'s" is enough for a series being a Fourier-Stieltjes series of a positive measure

Published on 15 Apr 2026 - 13:50

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Why does Fourier Transform use a negative exponent in its formula?

Published on 09 Apr 2026 - 14:52

58

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Some motivation on the Fourier series

Published on 13 Apr 2026 - 20:47

76

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Derivative of a distribution in $\mathcal{D}'(\mathbb{R})$

Published on 13 Apr 2026 - 14:15

39

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Heat equation in a three dimensional ball (for a Fourier analysis class)

Published on 10 Apr 2026 - 9:30

64

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Ways of computing $\int_{-\beta}^{\beta}dx\cot(x/2)\sin(n\pi x/\beta)$

Published on 16 Apr 2026 - 3:49

307

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Sup norm of Fourier transform of $ \frac{\sin |x|}{|x|^\lambda} \mathbb 1_{\{2^k\le |x| <2^{k+1}\}}, \ 0<\lambda<n $

Published on 13 Apr 2026 - 16:43

195

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Fourier Transform of self-similar functions

Published on 13 Apr 2026 - 9:56

31

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Under what circumstances can this happen?

Published on 14 Apr 2026 - 4:42

212

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Fourier transform of a Gaussian

Published on 11 Apr 2026 - 15:45

74

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2D Fourier Transform

Published on 11 Apr 2026 - 21:22

105

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Fourier Transform : complex or real?

Published on 11 Apr 2026 - 23:26

List Question

Show that the following limit of a Fourier looking integral exists

Fourier transform of the dilation of a distribution

$f(t)=\sum_{n=1}^{\infty}2\sin^{3}( \frac{\pi n}{2})\exp(\frac {-n^{2}\pi^{2}t}{2}).$ find $a,b $ such that $f(t)\sim ae^{-bt}$

Prove that "$\sigma_n(S,t)\ge 0$ for infinitely many $n$'s" is enough for a series being a Fourier-Stieltjes series of a positive measure

Why does Fourier Transform use a negative exponent in its formula?

Some motivation on the Fourier series

Derivative of a distribution in $\mathcal{D}'(\mathbb{R})$

Heat equation in a three dimensional ball (for a Fourier analysis class)

Ways of computing $\int_{-\beta}^{\beta}dx\cot(x/2)\sin(n\pi x/\beta)$

Sup norm of Fourier transform of $ \frac{\sin |x|}{|x|^\lambda} \mathbb 1_{\{2^k\le |x| <2^{k+1}\}}, \ 0<\lambda<n $

Fourier Transform of self-similar functions

Under what circumstances can this happen?

Fourier transform of a Gaussian

2D Fourier Transform

Fourier Transform : complex or real?

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