List questions from fourier-analysis

Published on 12 Apr 2026 - 23:51

50

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$L^1$ norm for product of cosines

Published on 14 Apr 2026 - 12:24

101

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Example - Homogeneity

Published on 10 May 2026 - 15:21

27

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$F_{s;I}=\frac1{2^{n-|I|}}\sum_{supp(t)\subset I^c}tr(\chi_tF_{s;I})\chi_t=\frac1{2^n}\sum_{supp(t)\subset I^c}tr(\chi_s\otimes\chi_tf)\chi_t$

Published on 16 Apr 2026 - 12:59

132

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Show that $1+\sum_{n=1}^{\infty} \frac{1}{n^2 (n+1)} = \frac{\pi^2}{6}$ without using the Basel Problem.

Published on 14 Apr 2026 - 7:01

37

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FOURIER TRANSFORM: How can I find the index of data points

Published on 27 Apr 2026 - 5:10

67

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Si function on Gibbs phenomenon

Published on 09 Apr 2026 - 8:19

62

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What kernels are unitary

Published on 13 Apr 2026 - 0:46

76

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Is there an "easy" proof of the existence of radial limits of functions in the hardy spaces $H^p$?

Published on 10 May 2026 - 23:41

77

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Is Plancherel's theorem on a Weighted $L^2$-space valid?

Published on 14 Apr 2026 - 12:15

116

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weakened $L^p$ interpolation using the Fourier transform?

Published on 12 Apr 2026 - 17:51

115

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Inverse Fourier transform of $\frac{\cos(x)}{x^2} $

Published on 16 Apr 2026 - 12:16

68

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The proof of decay rate of Fourier coefficients

Published on 12 Apr 2026 - 10:16

76

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How does $e^{-A(D)}$ and $D^{\alpha}$ commute?

Published on 11 Apr 2026 - 23:42

46

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How to see this function is supported in the open ball?

Published on 13 Apr 2026 - 18:01

List Question

Question about second derivate and Fourier transform

$L^1$ norm for product of cosines

Example - Homogeneity

$F_{s;I}=\frac1{2^{n-|I|}}\sum_{supp(t)\subset I^c}tr(\chi_tF_{s;I})\chi_t=\frac1{2^n}\sum_{supp(t)\subset I^c}tr(\chi_s\otimes\chi_tf)\chi_t$

Show that $1+\sum_{n=1}^{\infty} \frac{1}{n^2 (n+1)} = \frac{\pi^2}{6}$ without using the Basel Problem.

FOURIER TRANSFORM: How can I find the index of data points

Si function on Gibbs phenomenon

What kernels are unitary

Is there an "easy" proof of the existence of radial limits of functions in the hardy spaces $H^p$?

Is Plancherel's theorem on a Weighted $L^2$-space valid?

weakened $L^p$ interpolation using the Fourier transform?

Inverse Fourier transform of $\frac{\cos(x)}{x^2} $

The proof of decay rate of Fourier coefficients

How does $e^{-A(D)}$ and $D^{\alpha}$ commute?

How to see this function is supported in the open ball?

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