List questions from fourier-analysis

Published on 15 Apr 2026 - 5:30

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Fourier transform of $f(x)=x$ if $0<x\leq 1$ and $f(x)=0$ otherwise

Published on 15 Apr 2026 - 18:11

76

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Why is the Fourier transform of $f(x)=x$ on $[0,1]$, $0$ otherwise, apparently not square integrable?

Published on 15 Apr 2026 - 12:09

212

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How to show that $\int_{-\infty}^{\infty} \mathrm{d}^3 \textbf{k} \frac {e^{i \textbf{k x}}} {(2 \pi)^3} = \delta^3(x)$ in spherical coordinates?

Published on 15 Apr 2026 - 19:37

70

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How to understand this notation on Fourier transformation?

Published on 10 Apr 2026 - 12:10

2k

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Integration By Parts on a Fourier Transform

Published on 14 Apr 2026 - 5:21

91

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An inequality concerning the Fourier transform

Published on 09 Apr 2026 - 11:56

804

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Solve integral using Plancherel's formula

Published on 09 Apr 2026 - 3:13

90

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find the number of times the function is differentiable

Published on 13 Apr 2026 - 9:47

1.5k

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PCA produces sinusoids — what is the underlying cause?

Published on 25 Mar 2026 - 23:37

348

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Finding the Fourier Transform with Radial Coordinate

Published on 09 Apr 2026 - 14:31

245

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Gauss sum of a multiplication of two multiplicative characters of a finite field

Published on 10 May 2026 - 19:48

6.1k

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Good Kernel's Properties

Published on 12 Apr 2026 - 18:12

1.1k

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Poisson kernel approximates to the identity

Published on 12 Apr 2026 - 4:25

284

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Norm triangle inequality for convolutions proof

Published on 11 Apr 2026 - 14:10

List Question

Is $X(T) = A \sin(\omega_0 t + \Phi)$ mean ergodic?

Fourier transform of $f(x)=x$ if $0<x\leq 1$ and $f(x)=0$ otherwise

Why is the Fourier transform of $f(x)=x$ on $[0,1]$, $0$ otherwise, apparently not square integrable?

How to show that $\int_{-\infty}^{\infty} \mathrm{d}^3 \textbf{k} \frac {e^{i \textbf{k x}}} {(2 \pi)^3} = \delta^3(x)$ in spherical coordinates?

How to understand this notation on Fourier transformation?

Integration By Parts on a Fourier Transform

An inequality concerning the Fourier transform

Solve integral using Plancherel's formula

find the number of times the function is differentiable

PCA produces sinusoids — what is the underlying cause?

Finding the Fourier Transform with Radial Coordinate

Gauss sum of a multiplication of two multiplicative characters of a finite field

Good Kernel's Properties

Poisson kernel approximates to the identity

Norm triangle inequality for convolutions proof

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