Question

Derivation of $\hat{f}(\xi)=\frac{1}{\sqrt{2\pi}}\int_\limits{-\infty}^{\infty}f(t)\cos(t\xi)dt$

score 92 · Answer 1 · 2026-03-26 06:34:50

92

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Derivation of $\hat{f}(\xi)=\frac{1}{\sqrt{2\pi}}\int_\limits{-\infty}^{\infty}f(t)\cos(t\xi)dt$

Published on 26 Mar 2026 - 6:34

score 311 · Answer 2 · 2026-03-27 02:39:43

311

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What is inclusion relation between $L^p$ Sobolev spaces

Published on 27 Mar 2026 - 2:39

score 41 · Answer 3 · 2026-03-24 22:07:41

41

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Compute the coefficients of $\sum\limits_{n=1}^\infty A_n\sin\frac{n\pi x}{l}=\frac{x^2-x}{4}$

Published on 24 Mar 2026 - 22:07

score 115 · Answer 4 · 2026-03-29 14:07:16

115

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Showing that this version of the Fourier transoform ( on a circle ) is not surjective

Published on 29 Mar 2026 - 14:07

score 629 · Answer 5 · 2026-03-25 04:32:27

629

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Algorithm for converting complex sine wave to constituent simple sine waves

Published on 25 Mar 2026 - 4:32

score 46 · Answer 6 · 2026-03-25 17:42:20

46

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$\int_{\mathbb{T}} f(x) dx = \int_{\mathbb{T}} f(x-x_0) dx$ for $f \in C_0^{\infty}( \omega), \omega\subset \mathbb{T}$?

Published on 25 Mar 2026 - 17:42

score 144 · Answer 7 · 2026-03-26 04:51:56

144

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Prove that every sufficiently large Fourier coefficient is positive

Published on 26 Mar 2026 - 4:51

score 338 · Answer 8 · 2026-03-26 04:53:55

338

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Whats is the sum of series for each $0\le x\le 3$?

Published on 26 Mar 2026 - 4:53

score 337 · Answer 9 · 2026-03-26 04:50:30

337

Views

Injectivity of fourier coefficient map

Published on 26 Mar 2026 - 4:50

score 739 · Answer 10 · 2026-03-26 06:20:35

739

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Fourier transform of a function with exponential and powers

Published on 26 Mar 2026 - 6:20

score 2.1k · Answer 11 · 2026-03-26 06:32:35

2.1k

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How to find the sum $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots =\ ?$

Published on 26 Mar 2026 - 6:32

score 163 · Answer 12 · 2018-04-30 13:24:08

163

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Show that there does not exist $k\in L^1(\mathbb{T})$ such that $k*f=f$

Published on 30 Apr 2018 - 13:24

score 239 · Answer 13 · 2026-03-25 05:07:41

239

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Asymptotics for the Fourier transform of $\frac{1}{|x|} \frac{1}{e^{|x|} -1}$

Published on 25 Mar 2026 - 5:07

score 405 · Answer 14 · 2026-03-26 06:30:56

405

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Does Fourier cosine series converge in $L^2$ sense?

Published on 26 Mar 2026 - 6:30

score 394 · Answer 15 · 2026-03-25 19:06:26

394

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Prove that complex exponentials $(\phi_n(x)=\frac{1}{\sqrt{a}}e^{i\frac{2\pi nx}{a}})_{n=0, \pm 1, \pm2,...}$ are complete and orthonormal on $[0,a]$

Published on 25 Mar 2026 - 19:06

List Question

Derivation of $\hat{f}(\xi)=\frac{1}{\sqrt{2\pi}}\int_\limits{-\infty}^{\infty}f(t)\cos(t\xi)dt$

What is inclusion relation between $L^p$ Sobolev spaces

Compute the coefficients of $\sum\limits_{n=1}^\infty A_n\sin\frac{n\pi x}{l}=\frac{x^2-x}{4}$

Showing that this version of the Fourier transoform ( on a circle ) is not surjective

Algorithm for converting complex sine wave to constituent simple sine waves

$\int_{\mathbb{T}} f(x) dx = \int_{\mathbb{T}} f(x-x_0) dx$ for $f \in C_0^{\infty}( \omega), \omega\subset \mathbb{T}$?

Prove that every sufficiently large Fourier coefficient is positive

Whats is the sum of series for each $0\le x\le 3$?

Injectivity of fourier coefficient map

Fourier transform of a function with exponential and powers

How to find the sum $1+\frac{1}{2}-\frac{1}{4}-\frac{1}{5}+\frac{1}{7}+\frac{1}{8}-\frac{1}{10}-\frac{1}{11}+\cdots =\ ?$

Show that there does not exist $k\in L^1(\mathbb{T})$ such that $k*f=f$

Asymptotics for the Fourier transform of $\frac{1}{|x|} \frac{1}{e^{|x|} -1}$

Does Fourier cosine series converge in $L^2$ sense?

Prove that complex exponentials $(\phi_n(x)=\frac{1}{\sqrt{a}}e^{i\frac{2\pi nx}{a}})_{n=0, \pm 1, \pm2,...}$ are complete and orthonormal on $[0,a]$

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