Question

Orthonormal basis of the Schwartz space

score 599 · Answer 1 · 2026-04-13 18:56:33

Orthonormal basis of the Schwartz space

Published on 13 Apr 2026 - 18:56

score 19 · Answer 2 · 2026-04-15 14:41:09

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 102 · Answer 3 · 2026-04-10 05:17:01

102

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Fourier transform of creation operator on the Schwartz-space

Published on 10 Apr 2026 - 5:17

score 164 · Answer 4 · 2026-04-14 22:15:24

164

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

Published on 14 Apr 2026 - 22:15

score 113 · Answer 5 · 2026-04-13 04:45:43

113

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

Published on 13 Apr 2026 - 4:45

score 1.5k · Answer 6 · 2026-04-14 15:13:14

1.5k

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Example of a Schwartz function

Published on 14 Apr 2026 - 15:13

score 442 · Answer 7 · 2026-04-14 10:14:03

442

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Convergence of Schwartz functions and tempered distributions

Published on 14 Apr 2026 - 10:14

score 562 · Answer 8 · 2026-04-13 23:09:45

562

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Product of tempered distribution is again a tempered distribution?

Published on 13 Apr 2026 - 23:09

score 383 · Answer 9 · 2026-04-13 13:27:34

383

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

Published on 13 Apr 2026 - 13:27

score 53 · Answer 10 · 2026-04-14 14:30:51

53

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

Published on 14 Apr 2026 - 14:30

score 419 · Answer 11 · 2026-04-12 16:19:34

419

Views

Convolution a Schwartz function and a rapidly decreasing function

Published on 12 Apr 2026 - 16:19

score 1.1k · Answer 12 · 2026-04-17 05:32:55

1.1k

Views

Schwartz space is a Fréchet space

Published on 17 Apr 2026 - 5:32

score 259 · Answer 13 · 2026-04-11 23:02:26

259

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The behavior of Fourier transform near the origin

Published on 11 Apr 2026 - 23:02

score 131 · Answer 14 · 2026-04-16 11:40:04

131

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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 16 Apr 2026 - 11:40

score 920 · Answer 15 · 2026-04-11 12:01:56

920

Views

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

Published on 11 Apr 2026 - 12:01

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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