Question

Orthonormal basis of the Schwartz space

score 596 · Answer 1 · 2019-06-04 19:01:15

Orthonormal basis of the Schwartz space

Published on 04 Jun 2019 - 19:01

score 16 · Answer 2 · 2019-06-23 10:22:12

Show that any polynomial $P(x) \in E(\Omega) = C^{\infty}(\Omega)$ but $P(x)\notin S(\Omega)$, where $S(\Omega)$ is the Schwartz space.

score 99 · Answer 3 · 2019-06-25 18:17:14

99

Views

Fourier transform of creation operator on the Schwartz-space

Published on 25 Jun 2019 - 18:17

score 161 · Answer 4 · 2019-07-01 15:47:36

161

Views

$\mathscr{S}(\mathbb{R}) \text {is dense in } L^{2}(\mathbb{R})$

Published on 01 Jul 2019 - 15:47

score 110 · Answer 5 · 2019-07-27 15:41:50

110

Views

How to directly prove rapidly decay functions on $\mathbb{Z}$ is closed under convolution?

Published on 27 Jul 2019 - 15:41

score 1.5k · Answer 6 · 2019-08-09 15:15:51

1.5k

Views

Example of a Schwartz function

Published on 09 Aug 2019 - 15:15

score 439 · Answer 7 · 2019-08-13 17:50:13

439

Views

Convergence of Schwartz functions and tempered distributions

Published on 13 Aug 2019 - 17:50

score 559 · Answer 8 · 2019-08-16 00:40:59

559

Views

Product of tempered distribution is again a tempered distribution?

Published on 16 Aug 2019 - 0:40

score 381 · Answer 9 · 2019-08-19 14:25:44

381

Views

Is the inclusion of schwartz space on $L^{p}$ continous

Published on 19 Aug 2019 - 14:25

score 50 · Answer 10 · 2019-08-31 09:10:39

50

Views

Are $\xi \cdot \hat{u}(\xi)$ and $e^x \cdot u(x)$ bounded in $\mathbb{R}$?

Published on 31 Aug 2019 - 9:10

score 416 · Answer 11 · 2019-09-09 19:10:52

416

Views

Convolution a Schwartz function and a rapidly decreasing function

Published on 09 Sep 2019 - 19:10

score 1.1k · Answer 12 · 2019-09-30 01:52:32

1.1k

Views

Schwartz space is a Fréchet space

Published on 30 Sep 2019 - 1:52

score 256 · Answer 13 · 2014-03-13 01:56:45

256

Views

The behavior of Fourier transform near the origin

Published on 13 Mar 2014 - 1:56

score 128 · Answer 14 · 2014-04-07 11:55:46

128

Views

how to prove translation identity: $(\mathcal{F}^{-1}m\mathcal{F}f)(x)= e^{ikx}[\mathcal{F}^{-1}m(\cdot+k)\mathcal{F}(e^{-iky}f(y))](x)$?

Published on 07 Apr 2014 - 11:55

score 917 · Answer 15 · 2014-04-25 03:38:03

917

Views

An issue of applying Fubini's theorem in Fourier transform on Schwartz space.

Published on 25 Apr 2014 - 3:38

List Question

Orthonormal basis of the Schwartz space

Show that any polynomial $P(x) \in E(\Omega) = C^{\infty}(\Omega)$ but $P(x)\notin S(\Omega)$, where $S(\Omega)$ is the Schwartz space.

Fourier transform of creation operator on the Schwartz-space

$\mathscr{S}(\mathbb{R}) \text {is dense in } L^{2}(\mathbb{R})$

How to directly prove rapidly decay functions on $\mathbb{Z}$ is closed under convolution?

Example of a Schwartz function

Convergence of Schwartz functions and tempered distributions

Product of tempered distribution is again a tempered distribution?

Is the inclusion of schwartz space on $L^{p}$ continous

Are $\xi \cdot \hat{u}(\xi)$ and $e^x \cdot u(x)$ bounded in $\mathbb{R}$?

Convolution a Schwartz function and a rapidly decreasing function

Schwartz space is a Fréchet space

The behavior of Fourier transform near the origin

how to prove translation identity: $(\mathcal{F}^{-1}m\mathcal{F}f)(x)= e^{ikx}[\mathcal{F}^{-1}m(\cdot+k)\mathcal{F}(e^{-iky}f(y))](x)$?

An issue of applying Fubini's theorem in Fourier transform on Schwartz space.

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