Question

Find the Fourier Transform of $e^{i x t}$.

score 517 · Answer 1 · 2014-07-20 11:48:04

517

Views

Find the Fourier Transform of $e^{i x t}$.

Published on 20 Jul 2014 - 11:48

score 1.7k · Answer 2 · 2026-03-30 12:22:03

1.7k

Views

How to evaluate the integral $\int e^{ipx}e^{ipx} d^{3}x = 0$

Published on 30 Mar 2026 - 12:22

score 61 · Answer 3 · 2014-07-20 20:32:23

61

Views

Use the Fourier inversion formula to compute h(x) when $\hat{h}(x)=\frac{1}{(1+y^2)^2}$

Published on 20 Jul 2014 - 20:32

score 37 · Answer 4 · 2014-07-20 20:51:26

37

Views

In general, let $f \in L^2(-1,1)$ and let $g:R \to R$, $g(x)=f( \{ x \} )$. How are the Fourier transforms of f and g related?

Published on 20 Jul 2014 - 20:51

score 48 · Answer 5 · 2014-07-21 01:43:02

48

Views

Which of the functions below define a tempered distribution? The functions in a, b, c are defined in R.

Published on 21 Jul 2014 - 1:43

score 111 · Answer 6 · 2026-03-31 22:49:24

111

Views

About a property of weighted Sobolev spaces

Published on 31 Mar 2026 - 22:49

score 137 · Answer 7 · 2026-03-22 21:26:34

137

Views

Equivalence of Localized Fourier Restriction Estimates

Published on 22 Mar 2026 - 21:26

score 306 · Answer 8 · 2014-07-21 10:16:05

306

Views

$f\in L^{p}(\mathbb R)\cap C_{0}(\mathbb R); (1<p<\infty), g\in C^{\infty}_{c}(\mathbb R) \implies f\ast g \in C^{k}(\mathbb R)$?

Published on 21 Jul 2014 - 10:16

score 69 · Answer 9 · 2026-03-25 21:54:12

69

Views

How to choose, $\phi \in C^{\infty}_{c}(\mathbb R)$ such that its Fourier transform $\hat{\phi}$ is 1 in some neighbourhood of the given point?

Published on 25 Mar 2026 - 21:54

score 2.3k · Answer 10 · 2026-03-28 04:22:48

2.3k

Views

convolution of compactly supported continuous function with schwartz class function is again a Schwartz class function?

Published on 28 Mar 2026 - 4:22

score 63 · Answer 11 · 2026-04-06 14:19:44

63

Views

Can we identify Fourier transform of continuous compacltly supported functions with finte complex Borel measure?

Published on 06 Apr 2026 - 14:19

score 323 · Answer 12 · 2014-07-21 21:05:30

323

Views

Fourier transform of $L^2$ function

Published on 21 Jul 2014 - 21:05

score 188 · Answer 13 · 2014-07-21 21:46:43

188

Views

Calculating $\int_{-\pi}^{+\pi} e^{ixt} e^{-i \omega t} dt$

Published on 21 Jul 2014 - 21:46

score 1.6k · Answer 14 · 2026-04-02 22:12:22

1.6k

Views

$\int_{\mathbb R^{2}} |\int_{\mathbb R} (f_{r}(t-y)- f_{r}(t)) g(t-x) e^{-2\pi i w\cdot t} dt|dx dw \to 0 $ as $ r\to \infty $?

Published on 02 Apr 2026 - 22:12

score 369 · Answer 15 · 2026-03-26 22:12:11

369

Views

Parseval's theorem.

Published on 26 Mar 2026 - 22:12

List Question

Find the Fourier Transform of $e^{i x t}$.

How to evaluate the integral $\int e^{ipx}e^{ipx} d^{3}x = 0$

Use the Fourier inversion formula to compute h(x) when $\hat{h}(x)=\frac{1}{(1+y^2)^2}$

In general, let $f \in L^2(-1,1)$ and let $g:R \to R$, $g(x)=f( \{ x \} )$. How are the Fourier transforms of f and g related?

Which of the functions below define a tempered distribution? The functions in a, b, c are defined in R.

About a property of weighted Sobolev spaces

Equivalence of Localized Fourier Restriction Estimates

$f\in L^{p}(\mathbb R)\cap C_{0}(\mathbb R); (1<p<\infty), g\in C^{\infty}_{c}(\mathbb R) \implies f\ast g \in C^{k}(\mathbb R)$?

How to choose, $\phi \in C^{\infty}_{c}(\mathbb R)$ such that its Fourier transform $\hat{\phi}$ is 1 in some neighbourhood of the given point?

convolution of compactly supported continuous function with schwartz class function is again a Schwartz class function?

Can we identify Fourier transform of continuous compacltly supported functions with finte complex Borel measure?

Fourier transform of $L^2$ function

Calculating $\int_{-\pi}^{+\pi} e^{ixt} e^{-i \omega t} dt$

$\int_{\mathbb R^{2}} |\int_{\mathbb R} (f_{r}(t-y)- f_{r}(t)) g(t-x) e^{-2\pi i w\cdot t} dt|dx dw \to 0 $ as $ r\to \infty $?

Parseval's theorem.

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