Question

$\int_{\bf R}\frac{\partial u}{\partial t}(x,t)e^{-2\pi ix\xi}~dx=\frac{d}{dt}\int_{\bf R}u(x,t)e^{-2\pi ix\xi}~dx$

score 71 · Answer 1 · 2026-03-25 19:24:15

71

Views

$\int_{\bf R}\frac{\partial u}{\partial t}(x,t)e^{-2\pi ix\xi}~dx=\frac{d}{dt}\int_{\bf R}u(x,t)e^{-2\pi ix\xi}~dx$

Published on 25 Mar 2026 - 19:24

score 148 · Answer 2 · 2018-02-18 07:33:54

148

Views

$\frac{4}{\pi^{2}}\sum_{k~=1}^{N}\frac{1}{k}\le\|D_{N}\|_{L^{1}({\bf T})}\le3~-\frac{2}{\pi}+\frac{4}{\pi^{2}}\sum_{k~=1}^{N}\frac{1}{k}$

Published on 18 Feb 2018 - 7:33

score 90 · Answer 3 · 2026-03-25 02:58:55

90

Views

Condition for Fourier transform to exist?

Published on 25 Mar 2026 - 2:58

score 157 · Answer 4 · 2026-03-25 09:43:08

157

Views

$f(t)=\frac{\cos(\frac{3}{2}t)}{1+\cos^2(\frac{t}{4})}$ Find period and Fourier expansion

Published on 25 Mar 2026 - 9:43

score 1k · Answer 5 · 2026-03-25 04:39:22

1k

Views

Fourier transform to solve an integral $\frac{1}{(1+x^2)}\cdot e^{-ix}$

Published on 25 Mar 2026 - 4:39

score 1.6k · Answer 6 · 2026-03-22 23:59:37

1.6k

Views

To check whether the function is piecewise continuous or not

Published on 22 Mar 2026 - 23:59

score 117 · Answer 7 · 2026-03-27 03:07:53

117

Views

Orthogonality of Meyer Wavelets

Published on 27 Mar 2026 - 3:07

score 186 · Answer 8 · 2026-03-25 09:38:10

186

Views

Convolution of trigonometric polynomial $P$ with function $G$ such that $\widehat G(m)=m$

Published on 25 Mar 2026 - 9:38

score 35 · Answer 9 · 2026-03-25 04:38:10

35

Views

$\sum_j \sin(x_jt) \coth(\alpha x_j)$

Published on 25 Mar 2026 - 4:38

score 84 · Answer 10 · 2026-03-25 03:21:13

84

Views

Fourier transform of smoothed measure converges uniformly globally (not just on compact sets)?

Published on 25 Mar 2026 - 3:21

score 257 · Answer 11 · 2026-03-24 22:13:00

257

Views

Integration of the product of a function and the Heaviside function

Published on 24 Mar 2026 - 22:13

score 33 · Answer 12 · 2026-03-29 07:38:46

33

Views

System of equations from contour

Published on 29 Mar 2026 - 7:38

score 485 · Answer 13 · 2026-03-29 07:37:31

485

Views

Using Integration by Parts to Justify the Derivative of a Tempered Distribution

Published on 29 Mar 2026 - 7:37

score 677 · Answer 14 · 2026-03-25 04:40:13

677

Views

Regularity of a function from asymptotics of its Fourier transform?

Published on 25 Mar 2026 - 4:40

score 1.3k · Answer 15 · 2026-03-25 09:33:58

1.3k

Views

Fourier coefficients for an arbitrary period, different forms?

Published on 25 Mar 2026 - 9:33

List Question

$\int_{\bf R}\frac{\partial u}{\partial t}(x,t)e^{-2\pi ix\xi}~dx=\frac{d}{dt}\int_{\bf R}u(x,t)e^{-2\pi ix\xi}~dx$

$\frac{4}{\pi^{2}}\sum_{k~=1}^{N}\frac{1}{k}\le\|D_{N}\|_{L^{1}({\bf T})}\le3~-\frac{2}{\pi}+\frac{4}{\pi^{2}}\sum_{k~=1}^{N}\frac{1}{k}$

Condition for Fourier transform to exist?

$f(t)=\frac{\cos(\frac{3}{2}t)}{1+\cos^2(\frac{t}{4})}$ Find period and Fourier expansion

Fourier transform to solve an integral $\frac{1}{(1+x^2)}\cdot e^{-ix}$

To check whether the function is piecewise continuous or not

Orthogonality of Meyer Wavelets

Convolution of trigonometric polynomial $P$ with function $G$ such that $\widehat G(m)=m$

$\sum_j \sin(x_jt) \coth(\alpha x_j)$

Fourier transform of smoothed measure converges uniformly globally (not just on compact sets)?

Integration of the product of a function and the Heaviside function

System of equations from contour

Using Integration by Parts to Justify the Derivative of a Tempered Distribution

Regularity of a function from asymptotics of its Fourier transform?

Fourier coefficients for an arbitrary period, different forms?

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