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Question about derivation of Fourier transform

score 71 · Answer 1 · 2026-04-11 19:19:26

71

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Question about derivation of Fourier transform

Published on 11 Apr 2026 - 19:19

score 91 · Answer 2 · 2026-03-25 17:44:35

91

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Can the inverse Fourier transform $f(x)=\mathcal{F}_{\omega}^{-1}[F(\omega)](x)$ converge when $F(\omega)=\mathcal{F}_x[f(x)](\omega)$ doesn't?

Published on 25 Mar 2026 - 17:44

score 21 · Answer 3 · 2026-04-15 21:52:05

21

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1D power spectrum of field filtered by 3D filters

Published on 15 Apr 2026 - 21:52

score 59 · Answer 4 · 2026-04-15 09:56:53

59

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Mutual orthogonality of triangle waves

Published on 15 Apr 2026 - 9:56

score 28 · Answer 5 · 2026-04-15 11:33:26

28

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Computing the 2D greyscale image produced from putting a row and column of zeros between every two rows and two columns in the Fourier transform $F$

Published on 15 Apr 2026 - 11:33

score 71 · Answer 6 · 2026-04-12 16:11:47

71

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Relationship between Fourier inversion theorem and convergence of "nested Fourier series representations" of $f(x)$

Published on 12 Apr 2026 - 16:11

score 41 · Answer 7 · 2026-04-13 03:29:24

41

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Form of fourier series in 3D coordinate

Published on 13 Apr 2026 - 3:29

score 25 · Answer 8 · 2026-04-15 07:14:15

25

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Estimating L1 norm of a trigonometric polynomial related to Dirichlet kernel

Published on 15 Apr 2026 - 7:14

score 74 · Answer 9 · 2026-04-09 08:08:51

74

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The Heat Kernel $H_t(x)$ is a good kernel for $t \to 0$, understanding proof from Stein's Fourier Analysis

Published on 09 Apr 2026 - 8:08

score 33 · Answer 10 · 2026-04-14 04:31:21

33

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Approximating the surface measure of spheres via Fourier transform

Published on 14 Apr 2026 - 4:31

score 67 · Answer 11 · 2026-04-16 14:54:22

67

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Decay rate of $\vert x \vert^\alpha$ is $\mathcal{O}(\vert n \vert^{-1-\alpha})$

Published on 16 Apr 2026 - 14:54

score 117 · Answer 12 · 2026-04-11 09:40:04

117

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Solving Poisson equation with Fourier transform.

Published on 11 Apr 2026 - 9:40

score 49 · Answer 13 · 2026-04-08 22:33:15

49

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Can any function be written as a linear combination of only sines?

Published on 08 Apr 2026 - 22:33

score 58 · Answer 14 · 2026-04-12 22:24:22

58

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Translation invariant operators and Fourier transforms

Published on 12 Apr 2026 - 22:24

score 52 · Answer 15 · 2026-04-12 15:41:08

52

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On differentiability and Fourier coefficients; Vretblad

Published on 12 Apr 2026 - 15:41

List Question

Question about derivation of Fourier transform

Can the inverse Fourier transform $f(x)=\mathcal{F}_{\omega}^{-1}[F(\omega)](x)$ converge when $F(\omega)=\mathcal{F}_x[f(x)](\omega)$ doesn't?

1D power spectrum of field filtered by 3D filters

Mutual orthogonality of triangle waves

Computing the 2D greyscale image produced from putting a row and column of zeros between every two rows and two columns in the Fourier transform $F$

Relationship between Fourier inversion theorem and convergence of "nested Fourier series representations" of $f(x)$

Form of fourier series in 3D coordinate

Estimating L1 norm of a trigonometric polynomial related to Dirichlet kernel

The Heat Kernel $H_t(x)$ is a good kernel for $t \to 0$, understanding proof from Stein's Fourier Analysis

Approximating the surface measure of spheres via Fourier transform

Decay rate of $\vert x \vert^\alpha$ is $\mathcal{O}(\vert n \vert^{-1-\alpha})$

Solving Poisson equation with Fourier transform.

Can any function be written as a linear combination of only sines?

Translation invariant operators and Fourier transforms

On differentiability and Fourier coefficients; Vretblad

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