List questions from fourier-series

Published on 03 Apr 2015 - 13:15

118

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$\|fg\|_{A (\mathbb T)} \leq C \|f\|_{L^{2}} \|g\|_{A (\mathbb T)}$?

Published on 04 Apr 2015 - 7:24

73

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Can we expect $\|fg\|_{\mathcal{F}L^{1}} \leq C \|f\|_{L^{2}(\mathbb R)} \|g\|_{\mathcal{F}L^{1}}$?

Published on 05 Apr 2026 - 1:47

43

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Do I have to transform the solution into $u(x, y)$?

Published on 10 Apr 2026 - 20:07

145

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A trigonometric integral identity from Krylov's "Approximate Calculation of Integrals"

Published on 10 Apr 2026 - 1:02

164

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A difficult trigonometric integral involving absolute value

Published on 11 Apr 2026 - 11:52

272

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Writing a Fourier series of a $2\pi$-periodic function.

Published on 09 Apr 2026 - 14:52

144

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Show that $\widehat{f}(n)$ is zero for odd $n$

Published on 07 Apr 2015 - 17:41

198

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Show that the Fourier series is $\frac{8}{\pi} \sum_{k \;odd \ge 1} \frac{sin(k \theta)}{k^3} $

Published on 07 Apr 2015 - 18:32

75

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Compute the Fourier series of a piecewise function.

Published on 07 Apr 2015 - 19:27

59

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ODE with finite Fourier expansion periodic coefficients

Published on 11 Apr 2026 - 1:50

171

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Table of Fourier series

Published on 08 Apr 2015 - 16:16

706

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Chladni patterns

Published on 11 Apr 2026 - 22:47

360

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Solve differential equation using fourier series

Published on 10 Apr 2026 - 21:50

3.9k

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Integral using Parseval's Theorem

Published on 09 Apr 2015 - 12:06

List Question

Is there a closed-form of $\sum_{n=1}^{\infty} \frac{\sin(n)}{n^4}$

$\|fg\|_{A (\mathbb T)} \leq C \|f\|_{L^{2}} \|g\|_{A (\mathbb T)}$?

Can we expect $\|fg\|_{\mathcal{F}L^{1}} \leq C \|f\|_{L^{2}(\mathbb R)} \|g\|_{\mathcal{F}L^{1}}$?

Do I have to transform the solution into $u(x, y)$?

A trigonometric integral identity from Krylov's "Approximate Calculation of Integrals"

A difficult trigonometric integral involving absolute value

Writing a Fourier series of a $2\pi$-periodic function.

Show that $\widehat{f}(n)$ is zero for odd $n$

Show that the Fourier series is $\frac{8}{\pi} \sum_{k \;odd \ge 1} \frac{sin(k \theta)}{k^3} $

Compute the Fourier series of a piecewise function.

ODE with finite Fourier expansion periodic coefficients

Table of Fourier series

Chladni patterns

Solve differential equation using fourier series

Integral using Parseval's Theorem

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