List questions from fourier-analysis

Published on 08 Apr 2026 - 3:27

661

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log|x| is a tempered distribution

Published on 14 Apr 2026 - 22:12

60

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How to compute the following Fourier transform

Published on 11 Apr 2026 - 15:05

254

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Fourier transform on a complex torus

Published on 11 Apr 2026 - 8:48

1.1k

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Find best approximation of $\sin(\pi x)$ over $[0,1]$ with quadratic polynomial $a_0+a_1x+a_2x^2$

Published on 15 Apr 2026 - 10:59

738

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Discrete-time fourier transform as a periodic sum of fourier transform for different sampling

Published on 09 Apr 2026 - 11:43

71

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Derivative of Fourier transform: does the property exist

Published on 12 Apr 2026 - 0:26

48

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Fourier transformation of this equation

Published on 08 Apr 2026 - 19:38

68

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Proving the Fourier Transform of $h(-t) = H(f)^*$

Published on 11 Apr 2026 - 6:14

174

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How to go from Fourier to Chebyshev?

Published on 25 Mar 2026 - 14:06

208

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when defining continuous operators on distributions, why does the adjoint operator need to be continuous?

Published on 09 Apr 2026 - 20:40

121

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Writing an expectation in terms of Fourier Coefficients

Published on 09 Apr 2026 - 3:30

939

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Show that the Fejér Kernel $F_n$ is a good kernel and $\int_{0}^{1}F_n(x)dx = 1$

Published on 09 Apr 2026 - 8:09

144

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Why does the Dirichlet Kernel $D_N$, the sum of exponentials gives $\frac{1}{2\pi}\int_{-\pi}^{\pi}D_N(x)~dx =1$?

Published on 09 Apr 2026 - 8:10

51

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Prove that the linear operator $\Sigma_n$ on $B^\ast$ has norm $ \|\Sigma_n\|^{B^\ast}=1. $

Published on 13 Apr 2026 - 20:09

List Question

inner product and measure theory question

log|x| is a tempered distribution

How to compute the following Fourier transform

Fourier transform on a complex torus

Find best approximation of $\sin(\pi x)$ over $[0,1]$ with quadratic polynomial $a_0+a_1x+a_2x^2$

Discrete-time fourier transform as a periodic sum of fourier transform for different sampling

Derivative of Fourier transform: does the property exist

Fourier transformation of this equation

Proving the Fourier Transform of $h(-t) = H(f)^*$

How to go from Fourier to Chebyshev?

when defining continuous operators on distributions, why does the adjoint operator need to be continuous?

Writing an expectation in terms of Fourier Coefficients

Show that the Fejér Kernel $F_n$ is a good kernel and $\int_{0}^{1}F_n(x)dx = 1$

Why does the Dirichlet Kernel $D_N$, the sum of exponentials gives $\frac{1}{2\pi}\int_{-\pi}^{\pi}D_N(x)~dx =1$?

Prove that the linear operator $\Sigma_n$ on $B^\ast$ has norm $ \|\Sigma_n\|^{B^\ast}=1. $

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