Question

Inverse Fourier transform of $\Gamma(z)\zeta(2z)$

score 210 · Answer 1 · 2020-05-16 13:41:23

210

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Inverse Fourier transform of $\Gamma(z)\zeta(2z)$

Published on 16 May 2020 - 13:41

score 586 · Answer 2 · 2026-04-01 10:23:35

586

Views

Book recommendations for fourier series.

Published on 01 Apr 2026 - 10:23

score 83 · Answer 3 · 2026-03-30 09:48:27

83

Views

Approximating by convolution a function $f \in L^1(\mathbb{R})$ such that $\hat{f} \in L^1(\mathbb{R})$.

Published on 30 Mar 2026 - 9:48

score 104 · Answer 4 · 2020-05-18 06:00:24

104

Views

Fourier Transform in cylindrical coordinate system

Published on 18 May 2020 - 6:00

score 158 · Answer 5 · 2020-05-18 20:54:06

158

Views

How to prove that $\lim_{y \rightarrow \infty} \frac{\sin^2(xy)}{yx^2}=\pi \delta(x)$

Published on 18 May 2020 - 20:54

score 56 · Answer 6 · 2020-05-18 21:49:54

56

Views

How does this equation follow by taking Fourier transforms?

Published on 18 May 2020 - 21:49

score 307 · Answer 7 · 2020-05-18 22:56:36

307

Views

Fourier Transform of a function not in Schwartz Space

Published on 18 May 2020 - 22:56

score 2.2k · Answer 8 · 2020-05-19 16:22:32

2.2k

Views

Fourier transform $h(t) = e^{-2(t-1)}u(t-1)$

Published on 19 May 2020 - 16:22

score 151 · Answer 9 · 2026-04-01 02:53:37

151

Views

Lower bounding decay of Fourier transform of a discontinuous function

Published on 01 Apr 2026 - 2:53

score 179 · Answer 10 · 2020-05-20 21:46:22

179

Views

How can Discrete Fourier Transform yield negative frequencies?

Published on 20 May 2020 - 21:46

score 58 · Answer 11 · 2026-03-25 17:42:16

58

Views

Prove that $\mathcal{F}\{\cos(\omega_0 n)\}=\pi\sum_{k=-\infty}^{+\infty}[\delta(\omega-\omega_0-2\pi k)+\delta(\omega+\omega_0-2\pi k)]$

Published on 25 Mar 2026 - 17:42

score 99 · Answer 12 · 2026-03-25 12:15:16

99

Views

Is there a transform based on Mellin convolution analogous to the Hilbert transform which is based on Fourier convolution?

Published on 25 Mar 2026 - 12:15

score 123 · Answer 13 · 2026-03-27 21:19:15

123

Views

Condition for non-negative Fourier transform: $\mathcal{F} \exp(-|x|^a)(|x|^a\log(x)+\delta) \ge 0$

Published on 27 Mar 2026 - 21:19

score 128 · Answer 14 · 2020-05-22 19:21:57

128

Views

Fourier transform in polar coordinate

Published on 22 May 2020 - 19:21

score 52 · Answer 15 · 2020-05-23 00:27:42

52

Views

Show that $f$ is $m$-times differentiable with $f^{(m)}\in L^2(\mathbb T)$ provided $k-m>\frac{1}{2}$.

Published on 23 May 2020 - 0:27

List Question

Inverse Fourier transform of $\Gamma(z)\zeta(2z)$

Book recommendations for fourier series.

Approximating by convolution a function $f \in L^1(\mathbb{R})$ such that $\hat{f} \in L^1(\mathbb{R})$.

Fourier Transform in cylindrical coordinate system

How to prove that $\lim_{y \rightarrow \infty} \frac{\sin^2(xy)}{yx^2}=\pi \delta(x)$

How does this equation follow by taking Fourier transforms?

Fourier Transform of a function not in Schwartz Space

Fourier transform $h(t) = e^{-2(t-1)}u(t-1)$

Lower bounding decay of Fourier transform of a discontinuous function

How can Discrete Fourier Transform yield negative frequencies?

Prove that $\mathcal{F}\{\cos(\omega_0 n)\}=\pi\sum_{k=-\infty}^{+\infty}[\delta(\omega-\omega_0-2\pi k)+\delta(\omega+\omega_0-2\pi k)]$

Is there a transform based on Mellin convolution analogous to the Hilbert transform which is based on Fourier convolution?

Condition for non-negative Fourier transform: $\mathcal{F} \exp(-|x|^a)(|x|^a\log(x)+\delta) \ge 0$

Fourier transform in polar coordinate

Show that $f$ is $m$-times differentiable with $f^{(m)}\in L^2(\mathbb T)$ provided $k-m>\frac{1}{2}$.

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