Question

Construct a continuous function $f(x)$ periodic with period $2\pi$ such that the Fourier series of $f(x)$ is divergent at $x = 0$

score 86 · Answer 1 · 2026-03-26 19:02:50

86

Views

Construct a continuous function $f(x)$ periodic with period $2\pi$ such that the Fourier series of $f(x)$ is divergent at $x = 0$

Published on 26 Mar 2026 - 19:02

score 23 · Answer 2 · 2026-04-15 12:03:24

23

Views

Estimate $L^2$ norm of Fourier transform

Published on 15 Apr 2026 - 12:03

score 34 · Answer 3 · 2026-04-13 12:19:34

34

Views

Fourier transform of $L^{1}(\mathbb{R}^{n})$ functions in one variable at a time

Published on 13 Apr 2026 - 12:19

score 50 · Answer 4 · 2026-04-14 09:07:52

50

Views

Orthonormal basis of the Fourier Transform

Published on 14 Apr 2026 - 9:07

score 79 · Answer 5 · 2026-04-13 14:16:43

79

Views

How the Fourier transform show the frequency extent of $f(x)$?

Published on 13 Apr 2026 - 14:16

score 67 · Answer 6 · 2026-04-09 23:54:28

67

Views

The Connection between Fourier transform and Fourier series (derivation and Intuition)

Published on 09 Apr 2026 - 23:54

score 177 · Answer 7 · 2026-04-12 03:47:01

177

Views

Motivation for the selection of basis function of Fourier series

Published on 12 Apr 2026 - 3:47

score 18 · Answer 8 · 2026-04-17 15:00:37

18

Views

Vanishing of an exponential sum $f(x)=\sum_{k=1}^n a_k e^{ik b_k}$ on sets of the form $\{ \alpha l : l = -m, \dots, m \}$

Published on 17 Apr 2026 - 15:00

score 68 · Answer 9 · 2026-04-11 05:21:55

68

Views

Is it true that if $h \in L^{1}(\mathbb{R})$ such that $\hat{h} \in L^{2}(\mathbb{R})$ then in fact $h \in L^{2}(\mathbb{R})$

Published on 11 Apr 2026 - 5:21

score 38 · Answer 10 · 2026-04-10 18:26:50

38

Views

Solution to convolution integral equation

Published on 10 Apr 2026 - 18:26

score 54 · Answer 11 · 2026-04-13 19:28:10

54

Views

Reference for the following claim

Published on 13 Apr 2026 - 19:28

score 80 · Answer 12 · 2026-04-09 12:55:13

80

Views

Integral Equation and Fourier Analysis

Published on 09 Apr 2026 - 12:55

score 85 · Answer 13 · 2026-04-14 05:56:25

85

Views

Newton series and Fourier transform, is there an analogy?

Published on 14 Apr 2026 - 5:56

score 142 · Answer 14 · 2026-04-13 03:11:39

142

Views

Inequality of fourier coefficients

Published on 13 Apr 2026 - 3:11

score 300 · Answer 15 · 2026-04-11 08:46:41

300

Views

Laplace equation in 2D for a continuous source: is there a continuous solution?

Published on 11 Apr 2026 - 8:46

List Question

Construct a continuous function $f(x)$ periodic with period $2\pi$ such that the Fourier series of $f(x)$ is divergent at $x = 0$

Estimate $L^2$ norm of Fourier transform

Fourier transform of $L^{1}(\mathbb{R}^{n})$ functions in one variable at a time

Orthonormal basis of the Fourier Transform

How the Fourier transform show the frequency extent of $f(x)$?

The Connection between Fourier transform and Fourier series (derivation and Intuition)

Motivation for the selection of basis function of Fourier series

Vanishing of an exponential sum $f(x)=\sum_{k=1}^n a_k e^{ik b_k}$ on sets of the form $\{ \alpha l : l = -m, \dots, m \}$

Is it true that if $h \in L^{1}(\mathbb{R})$ such that $\hat{h} \in L^{2}(\mathbb{R})$ then in fact $h \in L^{2}(\mathbb{R})$

Solution to convolution integral equation

Reference for the following claim

Integral Equation and Fourier Analysis

Newton series and Fourier transform, is there an analogy?

Inequality of fourier coefficients

Laplace equation in 2D for a continuous source: is there a continuous solution?

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