Question

When does $|\hat{f}(n)|$ decrease to $0$ monotonically; while $\hat{f}(n)$s are Fourier coefficients of $f$?

score 44 · Answer 1 · 2026-04-16 02:58:27

44

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When does $|\hat{f}(n)|$ decrease to $0$ monotonically; while $\hat{f}(n)$s are Fourier coefficients of $f$?

Published on 16 Apr 2026 - 2:58

score 85 · Answer 2 · 2026-04-15 14:00:15

85

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Heisenberg Inequality for $L^2$ functions

Published on 15 Apr 2026 - 14:00

score 77 · Answer 3 · 2026-04-10 19:09:30

77

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An integration from a fourier transformation

Published on 10 Apr 2026 - 19:09

score 111 · Answer 4 · 2026-04-28 11:23:06

111

Views

Spatial localization of Littlewood--Paley decomposition. Proving the fractional Hardy inequality.

Published on 28 Apr 2026 - 11:23

score 129 · Answer 5 · 2026-04-10 18:15:06

129

Views

A tent shaped function and Fourier coefficients

Published on 10 Apr 2026 - 18:15

score 89 · Answer 6 · 2026-04-15 09:35:00

89

Views

Justifying validity of use of integration by parts in proof of Heisenberg's inequality

Published on 15 Apr 2026 - 9:35

score 104 · Answer 7 · 2026-04-16 22:23:02

104

Views

Integrating $\int_{0}^{r} \sqrt{r^2 - x^2} \cos(wx)dx$

Published on 16 Apr 2026 - 22:23

score 20 · Answer 8 · 2026-04-14 05:48:34

20

Views

How can I design a certainty or transparency weighted Fast Fourier transform?

Published on 14 Apr 2026 - 5:48

score 46 · Answer 9 · 2026-03-26 16:05:18

46

Views

Recreating an image with a Haar function basis instead of Fourier basis

Published on 26 Mar 2026 - 16:05

score 45 · Answer 10 · 2026-04-16 14:57:57

45

Views

Lower bound on $|\sum_{x \in X} \phi(x) - \int_{\mathbb{R^2}} \phi(x) dx |$ for $\phi$ smooth.

Published on 16 Apr 2026 - 14:57

score 93 · Answer 11 · 2026-04-15 23:30:02

93

Views

Bound for Fourier coefficient of a $C^1$ but not $C^2$ function

Published on 15 Apr 2026 - 23:30

score 63 · Answer 12 · 2026-04-15 01:40:54

63

Views

Is there exist a function $f\in C^1(\mathbb{T})$ such that $\displaystyle\sum_{k \in \mathbb{Z}}|\widehat{f}(k)| \to \infty$?

Published on 15 Apr 2026 - 1:40

score 31 · Answer 13 · 2026-04-09 13:06:29

31

Views

About proper functions and Fourier transforms

Published on 09 Apr 2026 - 13:06

score 98 · Answer 14 · 2026-04-12 20:19:05

98

Views

Fourier transform of $e^{i \alpha x^2}$ with $\alpha$ real

Published on 12 Apr 2026 - 20:19

score 81 · Answer 15 · 2026-04-11 10:50:06

81

Views

Solve variational equation using the Fourier transform

Published on 11 Apr 2026 - 10:50

List Question

When does $|\hat{f}(n)|$ decrease to $0$ monotonically; while $\hat{f}(n)$s are Fourier coefficients of $f$?

Heisenberg Inequality for $L^2$ functions

An integration from a fourier transformation

Spatial localization of Littlewood--Paley decomposition. Proving the fractional Hardy inequality.

A tent shaped function and Fourier coefficients

Justifying validity of use of integration by parts in proof of Heisenberg's inequality

Integrating $\int_{0}^{r} \sqrt{r^2 - x^2} \cos(wx)dx$

How can I design a certainty or transparency weighted Fast Fourier transform?

Recreating an image with a Haar function basis instead of Fourier basis

Lower bound on $|\sum_{x \in X} \phi(x) - \int_{\mathbb{R^2}} \phi(x) dx |$ for $\phi$ smooth.

Bound for Fourier coefficient of a $C^1$ but not $C^2$ function

Is there exist a function $f\in C^1(\mathbb{T})$ such that $\displaystyle\sum_{k \in \mathbb{Z}}|\widehat{f}(k)| \to \infty$?

About proper functions and Fourier transforms

Fourier transform of $e^{i \alpha x^2}$ with $\alpha$ real

Solve variational equation using the Fourier transform

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