Question

An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis

score 160 · Answer 1 · 2026-05-05 12:49:45

160

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An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis

Published on 05 May 2026 - 12:49

score 83 · Answer 2 · 2026-05-10 09:52:54

83

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Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)

Published on 10 May 2026 - 9:52

score 74 · Answer 3 · 2026-05-05 07:26:04

74

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How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?

Published on 05 May 2026 - 7:26

score 110 · Answer 4 · 2026-05-05 22:31:16

110

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Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$

Published on 05 May 2026 - 22:31

score 420 · Answer 5 · 2026-05-04 15:07:43

420

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Proving the sharper form of the Lebesgue Differentiation Theorem

Published on 04 May 2026 - 15:07

score 1k · Answer 6 · 2026-05-05 09:20:05

1k

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Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi

Published on 05 May 2026 - 9:20

score 127 · Answer 7 · 2026-05-07 19:18:27

127

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Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $

Published on 07 May 2026 - 19:18

score 77 · Answer 8 · 2026-05-05 05:32:57

77

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Taking the Discrete Inverse Fourier Transform of a Continuous Forward Transform

Published on 05 May 2026 - 5:32

score 756 · Answer 9 · 2026-05-07 12:44:55

756

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Is $x(t) = \sin(3t) + \cos\left({2\over3}t\right) + \cos(\pi t)$ periodic?

Published on 07 May 2026 - 12:44

score 300 · Answer 10 · 2026-05-07 11:33:56

300

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Translation of the work of Gauss where the fast Fourier transform algorithm first appeared

Published on 07 May 2026 - 11:33

score 139 · Answer 11 · 2026-04-29 12:23:50

139

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convergence of fourier series.

Published on 29 Apr 2026 - 12:23

score 1.2k · Answer 12 · 2026-05-13 07:43:57

1.2k

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The convolution theorem for fourier series.:$ \widehat{f*g}(x) =2π\hat{g}(x)\cdot\hat{f}(x) $

Published on 13 May 2026 - 7:43

score 431 · Answer 13 · 2026-05-04 18:46:18

431

Views

Arcsin of a number greater than one

Published on 04 May 2026 - 18:46

score 302 · Answer 14 · 2026-05-03 02:33:55

302

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Sobolev space $H^s(Q)$ is Hilbert

Published on 03 May 2026 - 2:33

score 74 · Answer 15 · 2026-05-11 03:07:55

74

Views

Expanding $\left| [\widehat{f}( \xi + h) - \widehat{f}( \xi)]/h - [- 2 \pi i f(x)]^{\wedge}(\xi) \right|$ into one integral

Published on 11 May 2026 - 3:07

List Question

An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis

Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)

How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?

Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$

Proving the sharper form of the Lebesgue Differentiation Theorem

Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi

Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $

Taking the Discrete Inverse Fourier Transform of a Continuous Forward Transform

Is $x(t) = \sin(3t) + \cos\left({2\over3}t\right) + \cos(\pi t)$ periodic?

Translation of the work of Gauss where the fast Fourier transform algorithm first appeared

convergence of fourier series.

The convolution theorem for fourier series.:$ \widehat{f*g}(x) =2π\hat{g}(x)\cdot\hat{f}(x) $

Arcsin of a number greater than one

Sobolev space $H^s(Q)$ is Hilbert

Expanding $\left| [\widehat{f}( \xi + h) - \widehat{f}( \xi)]/h - [- 2 \pi i f(x)]^{\wedge}(\xi) \right|$ into one integral

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