Question

Fourier transform of $\frac{x_i^2}{|x|^2}$

score 139 · Answer 1 · 2026-03-28 06:40:47

139

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Fourier transform of $\frac{x_i^2}{|x|^2}$

Published on 28 Mar 2026 - 6:40

score 115 · Answer 2 · 2014-05-12 10:02:07

115

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Why does $\overline{\langle f, \phi_n\rangle }\langle f, \phi_n\rangle = |\langle f, \phi_n\rangle|^2$

Published on 12 May 2014 - 10:02

score 47 · Answer 3 · 2014-05-12 13:11:56

47

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Understanding a Fourier analysis problem

Published on 12 May 2014 - 13:11

score 178 · Answer 4 · 2014-05-11 18:59:58

178

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Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$

Published on 11 May 2014 - 18:59

score 276 · Answer 5 · 2026-03-28 02:04:47

276

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Proving that a set $\{\psi_n(x)\}_1^\infty = \{\sqrt{c}\;\phi_n(cx+d)\}_1^\infty$ is an orthonormal basis

Published on 28 Mar 2026 - 2:04

score 1k · Answer 6 · 2014-05-13 09:11:22

1k

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How to use FFT algorithm

Published on 13 May 2014 - 9:11

score 1.4k · Answer 7 · 2026-03-28 02:04:35

1.4k

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Proving that orthonormal set is an orthonormal basis

Published on 28 Mar 2026 - 2:04

score 221 · Answer 8 · 2026-03-30 21:07:12

221

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Half range expansion

Published on 30 Mar 2026 - 21:07

score 124 · Answer 9 · 2026-03-31 04:09:28

124

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Fourier series, estimate the values of $a_0$, $a_n$ and $b_n$.

Published on 31 Mar 2026 - 4:09

score 161 · Answer 10 · 2014-05-13 19:17:50

161

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How to integrate this fourier transform?

Published on 13 May 2014 - 19:17

score 738 · Answer 11 · 2014-05-14 03:55:38

738

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$\sum_{n=1}^\infty \frac{1}{n^4}=\frac{\pi^4}{90}$

Published on 14 May 2014 - 3:55

score 239 · Answer 12 · 2014-05-14 05:05:26

239

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Question about the weak (1,1) bound for the Hilbert Transform (Javier Duoandikoetxea's Fourier Analysis)

Published on 14 May 2014 - 5:05

score 211 · Answer 13 · 2026-03-31 04:00:12

211

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Let $f(x) = |\cos(x)|$. Prove the corresponding Fourier series converge point-wise or uniform and show identity.

Published on 31 Mar 2026 - 4:00

score 5.7k · Answer 14 · 2014-05-14 17:44:33

5.7k

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Fourier transform of $e^{-|t|}\sin(t)$

Published on 14 May 2014 - 17:44

score 155 · Answer 15 · 2014-05-14 19:25:31

155

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Limit of an integration formula

Published on 14 May 2014 - 19:25

List Question

Fourier transform of $\frac{x_i^2}{|x|^2}$

Why does $\overline{\langle f, \phi_n\rangle }\langle f, \phi_n\rangle = |\langle f, \phi_n\rangle|^2$

Understanding a Fourier analysis problem

Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$

Proving that a set $\{\psi_n(x)\}_1^\infty = \{\sqrt{c}\;\phi_n(cx+d)\}_1^\infty$ is an orthonormal basis

How to use FFT algorithm

Proving that orthonormal set is an orthonormal basis

Half range expansion

Fourier series, estimate the values of $a_0$, $a_n$ and $b_n$.

How to integrate this fourier transform?

$\sum_{n=1}^\infty \frac{1}{n^4}=\frac{\pi^4}{90}$

Question about the weak (1,1) bound for the Hilbert Transform (Javier Duoandikoetxea's Fourier Analysis)

Let $f(x) = |\cos(x)|$. Prove the corresponding Fourier series converge point-wise or uniform and show identity.

Fourier transform of $e^{-|t|}\sin(t)$

Limit of an integration formula

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