Question

Behavior of the Fourier coefficients at $\infty$ for a particular function $f$

score 47 · Answer 1 · 2026-04-15 04:00:08

47

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Behavior of the Fourier coefficients at $\infty$ for a particular function $f$

Published on 15 Apr 2026 - 4:00

score 2.4k · Answer 2 · 2026-05-10 23:34:40

2.4k

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Fourier transform of single and double slit functions

Published on 10 May 2026 - 23:34

score 456 · Answer 3 · 2026-05-10 15:56:21

456

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Radial derivative of the characteristic function of the unit disc in $\mathbb R^2$.

Published on 10 May 2026 - 15:56

score 366 · Answer 4 · 2026-05-10 20:53:06

366

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Explanation of an answer in "Fourier transform of a radial function".

Published on 10 May 2026 - 20:53

score 63 · Answer 5 · 2026-05-10 22:29:21

63

Views

Easy integral inequality

Published on 10 May 2026 - 22:29

score 132 · Answer 6 · 2026-05-10 14:32:33

132

Views

Differentiability of the Fourier series of $(x^2-1)^2$ on [-1,1)

Published on 10 May 2026 - 14:32

score 847 · Answer 7 · 2026-04-09 17:23:38

847

Views

Fourier transform with compact support!!

Published on 09 Apr 2026 - 17:23

score 106 · Answer 8 · 2026-05-13 22:44:03

106

Views

Showing that $\{ \psi_i \}$ forms an orthonormal basis iff $\{ \widehat{\psi}_i \}$ forms an orthonormal basis in $L^2(\mathbb{R})$

Published on 13 May 2026 - 22:44

score 411 · Answer 9 · 2026-05-11 04:18:05

411

Views

Fourier-type series representation of "quasi-periodic" functions

Published on 11 May 2026 - 4:18

score 43 · Answer 10 · 2026-05-10 23:40:50

43

Views

let $T\subseteq [-\pi,\pi]$ be any countable set . show that there is a $f\in C(\mathbb{T})$ such that $S_N f(x)$ diverge at each $x\in {T}$

Published on 10 May 2026 - 23:40

score 421 · Answer 11 · 2026-05-10 20:50:46

421

Views

Inverse Fourier transform of a rational function

Published on 10 May 2026 - 20:50

score 554 · Answer 12 · 2026-04-11 14:38:39

554

Views

A question from Stein's Fourier analysis, Chapter 2, Exercise 11

Published on 11 Apr 2026 - 14:38

score 268 · Answer 13 · 2026-04-14 05:53:45

268

Views

Derivative of a Multivariate Heaviside unit step function

Published on 14 Apr 2026 - 5:53

score 41 · Answer 14 · 2026-04-14 10:56:01

41

Views

Understanding a part of the proof that $\xi^{\alpha}(\mathcal F \varphi)(\xi) = (-i)^{|\alpha|} \mathcal F (D^{\alpha}\varphi)(\xi)$

Published on 14 Apr 2026 - 10:56

score 62 · Answer 15 · 2026-05-13 11:42:01

62

Views

reshape $(2\pi)^{-n/2} \int_{\mathbb R^n} \mathcal F(\varphi) (\xi) e^{- \frac{\varepsilon^2|\xi|^2}{2}} e^{i\langle x, \xi \rangle} d\xi$

Published on 13 May 2026 - 11:42

List Question

Behavior of the Fourier coefficients at $\infty$ for a particular function $f$

Fourier transform of single and double slit functions

Radial derivative of the characteristic function of the unit disc in $\mathbb R^2$.

Explanation of an answer in "Fourier transform of a radial function".

Easy integral inequality

Differentiability of the Fourier series of $(x^2-1)^2$ on [-1,1)

Fourier transform with compact support!!

Showing that $\{ \psi_i \}$ forms an orthonormal basis iff $\{ \widehat{\psi}_i \}$ forms an orthonormal basis in $L^2(\mathbb{R})$

Fourier-type series representation of "quasi-periodic" functions

let $T\subseteq [-\pi,\pi]$ be any countable set . show that there is a $f\in C(\mathbb{T})$ such that $S_N f(x)$ diverge at each $x\in {T}$

Inverse Fourier transform of a rational function

A question from Stein's Fourier analysis, Chapter 2, Exercise 11

Derivative of a Multivariate Heaviside unit step function

Understanding a part of the proof that $\xi^{\alpha}(\mathcal F \varphi)(\xi) = (-i)^{|\alpha|} \mathcal F (D^{\alpha}\varphi)(\xi)$

reshape $(2\pi)^{-n/2} \int_{\mathbb R^n} \mathcal F(\varphi) (\xi) e^{- \frac{\varepsilon^2|\xi|^2}{2}} e^{i\langle x, \xi \rangle} d\xi$

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