Question

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

score 44 · Answer 1 · 2018-03-18 11:05:14

44

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

Published on 18 Mar 2018 - 11:05

score 2.4k · Answer 2 · 2026-03-25 09:25:30

2.4k

Views

Fourier transform of single and double slit functions

Published on 25 Mar 2026 - 9:25

score 453 · Answer 3 · 2026-03-25 03:02:51

453

Views

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

Published on 25 Mar 2026 - 3:02

score 363 · Answer 4 · 2026-03-25 11:16:14

363

Views

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

Published on 25 Mar 2026 - 11:16

score 58 · Answer 5 · 2026-03-25 12:47:13

58

Views

Easy integral inequality

Published on 25 Mar 2026 - 12:47

score 129 · Answer 6 · 2026-03-25 14:24:42

129

Views

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

Published on 25 Mar 2026 - 14:24

score 844 · Answer 7 · 2018-03-19 14:47:05

844

Views

Fourier transform with compact support!!

Published on 19 Mar 2018 - 14:47

score 103 · Answer 8 · 2026-03-29 09:11:54

103

Views

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

Published on 29 Mar 2026 - 9:11

score 408 · Answer 9 · 2026-03-25 12:54:59

408

Views

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

Published on 25 Mar 2026 - 12:54

score 40 · Answer 10 · 2026-03-25 12:49:40

40

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 25 Mar 2026 - 12:49

score 418 · Answer 11 · 2026-03-25 11:10:50

418

Views

Inverse Fourier transform of a rational function

Published on 25 Mar 2026 - 11:10

score 551 · Answer 12 · 2018-03-22 06:00:02

551

Views

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

Published on 22 Mar 2018 - 6:00

score 265 · Answer 13 · 2018-03-22 09:58:21

265

Views

Derivative of a Multivariate Heaviside unit step function

Published on 22 Mar 2018 - 9:58

score 39 · Answer 14 · 2026-03-29 04:44:08

39

Views

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

Published on 29 Mar 2026 - 4:44

score 53 · Answer 15 · 2026-03-25 08:23:19

53

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 25 Mar 2026 - 8:23

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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