List questions from harmonic-analysis

51

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Let $u\in C^\infty_0(\mathbb{R}^d)$, then show that $u(0)=\iint u(x)e^{-2\pi ix\cdot\xi}\,\mathrm{d}x\,\mathrm{d}\xi$.

Published on 27 Feb 2017 - 16:05

96

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Is solution of $div(k(x,y) \nabla(u(x,y)))=0$ harmonic function, for $k(x,y) > 0$?

Published on 29 Mar 2026 - 20:02

254

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Further smoothness conditions on $f$ imply better decay of Fourier Coefficients.

Published on 02 Mar 2017 - 14:59

111

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Riesz transform equivalent form

Published on 02 Mar 2017 - 18:27

1.3k

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What can be said about an $L^2$ function whose Fourier series is zero almost everywhere?

Published on 05 Mar 2017 - 5:15

325

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$L^{p} (\mathbb T)$ is complete.

Published on 06 Mar 2017 - 7:22

169

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Question about relationship between $\ell^ p$ spaces and Fourier coefficients.

Published on 06 Mar 2017 - 19:01

1.2k

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Given a Schwartz function, is it always possible to write it as a product of two Schwartz function?

Published on 26 Mar 2026 - 10:46

4.7k

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Uniqueness Of Fourier Series.

Published on 07 Mar 2017 - 15:54

2.2k

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Du-Bois- Reymond Function.

Published on 07 Mar 2017 - 16:28

956

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The nth Fourier Coefficient For Poisson Kernel.

Published on 07 Mar 2017 - 16:51

346

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What kind of $\mathcal{L}^1$ function has bounded Hilbert transform?

Published on 08 Mar 2017 - 11:53

395

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Theorem 2.1 in Stein and Shakarachi Fourier Analysis.(uniqueness of Fourier Series)

Published on 09 Mar 2017 - 4:16

56

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The idea of the proof of a theorem.

Published on 09 Mar 2017 - 4:37

745

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The idea of the proof of theorem 2.1 in Stein and Shakarchi' Fourier Analysis book

Published on 09 Mar 2017 - 4:58

List Question

Let $u\in C^\infty_0(\mathbb{R}^d)$, then show that $u(0)=\iint u(x)e^{-2\pi ix\cdot\xi}\,\mathrm{d}x\,\mathrm{d}\xi$.

Is solution of $div(k(x,y) \nabla(u(x,y)))=0$ harmonic function, for $k(x,y) > 0$?

Further smoothness conditions on $f$ imply better decay of Fourier Coefficients.

Riesz transform equivalent form

What can be said about an $L^2$ function whose Fourier series is zero almost everywhere?

$L^{p} (\mathbb T)$ is complete.

Question about relationship between $\ell^ p$ spaces and Fourier coefficients.

Given a Schwartz function, is it always possible to write it as a product of two Schwartz function?

Uniqueness Of Fourier Series.

Du-Bois- Reymond Function.

The nth Fourier Coefficient For Poisson Kernel.

What kind of $\mathcal{L}^1$ function has bounded Hilbert transform?

Theorem 2.1 in Stein and Shakarachi Fourier Analysis.(uniqueness of Fourier Series)

The idea of the proof of a theorem.

The idea of the proof of theorem 2.1 in Stein and Shakarchi' Fourier Analysis book

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