List questions from fourier-analysis

Published on 14 Apr 2026 - 3:49

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Derivative of function with Fourier transform

Published on 12 Apr 2026 - 21:53

47

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Compute $\sum_{n=1}^\infty \frac{1}{n^2}$ and $\sum_{n\geq 1,\ k\rm\ odd}\frac{1}{n^2}$ using fourier series.

Published on 13 Apr 2026 - 21:45

147

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Why and when is $ e^{- |x|^2} = \int d \omega e^{i \omega x} e^{-|\omega|^2 \gamma}$ true?

Published on 16 Apr 2026 - 0:54

1.6k

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Complex exponential series convergence $\sum_{n=0}^{\infty} \frac{z^n}{n!}$

Published on 14 Apr 2026 - 21:46

1.3k

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An exercise from Stein and Shakarchi's "Fourier Analysis" (exercise 14, chapter 8)

Published on 10 Apr 2026 - 6:14

427

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Fourier-transform of non-analytic function

Published on 11 Apr 2026 - 4:38

591

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Fourier transform (2D boson propagator in Euclidean space)

Published on 10 Apr 2026 - 9:24

88

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If $f \in L^1$ and $f$ is everywhere strictly positive, then does it follow that $|\widehat{f}(y)| < \widehat{f}(0)$ for $y \neq 0$?

Published on 16 Apr 2026 - 8:24

3.1k

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Fourier transform and Heisenberg's inequality.

Published on 11 Apr 2026 - 23:26

208

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Is $H^1$ a subspace of $L^2(-\pi, \pi)$?

Published on 14 Apr 2026 - 0:30

20

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Does $\sup_n r_2(E,n)<\infty$ imply $\Lambda(4)$?

Published on 25 Apr 2026 - 4:33

33

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solving 1D equation

Published on 11 Apr 2026 - 19:40

233

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How to take the Fourier transform of this distribution?

Published on 10 Apr 2026 - 19:53

36

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Intuition for matrix representation of deterministic sinusoidal cycle

Published on 10 Apr 2026 - 23:07

List Question

Integrating $e^{-(t|k|^\alpha+ixk)} $ with respect to $k$

Derivative of function with Fourier transform

Compute $\sum_{n=1}^\infty \frac{1}{n^2}$ and $\sum_{n\geq 1,\ k\rm\ odd}\frac{1}{n^2}$ using fourier series.

Why and when is $ e^{- |x|^2} = \int d \omega e^{i \omega x} e^{-|\omega|^2 \gamma}$ true?

Complex exponential series convergence $\sum_{n=0}^{\infty} \frac{z^n}{n!}$

An exercise from Stein and Shakarchi's "Fourier Analysis" (exercise 14, chapter 8)

Fourier-transform of non-analytic function

Fourier transform (2D boson propagator in Euclidean space)

If $f \in L^1$ and $f$ is everywhere strictly positive, then does it follow that $|\widehat{f}(y)| < \widehat{f}(0)$ for $y \neq 0$?

Fourier transform and Heisenberg's inequality.

Is $H^1$ a subspace of $L^2(-\pi, \pi)$?

Does $\sup_n r_2(E,n)<\infty$ imply $\Lambda(4)$?

solving 1D equation

How to take the Fourier transform of this distribution?

Intuition for matrix representation of deterministic sinusoidal cycle

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