Question

Changing order of integration in the Fourier inversion formula for the Schwartz functions

score 271 · Answer 1 · 2017-02-26 21:24:15

271

Views

Changing order of integration in the Fourier inversion formula for the Schwartz functions

Published on 26 Feb 2017 - 21:24

score 50 · Answer 2 · 2017-03-06 12:24:23

50

Views

If each $f_n$ is radial Schwartz, and $\|f_n\|_{L^{\infty}} \geq 1,$ can we choose $\{x_n\}$ bounded with $|f_n(x_n)|\geq 1$?

Published on 06 Mar 2017 - 12:24

score 1.2k · Answer 3 · 2017-03-06 22:18:56

1.2k

Views

Given a Schwartz function, is it always possible to write it as a product of two Schwartz function?

Published on 06 Mar 2017 - 22:18

score 324 · Answer 4 · 2017-03-17 15:08:50

324

Views

Is this a tempered distribution?

Published on 17 Mar 2017 - 15:08

score 298 · Answer 5 · 2017-03-22 23:21:06

298

Views

Is $\frac{1}{H(x) \pm i0}$ a distribution if $|\nabla H| \neq 0$ for $H(x)=0$?

Published on 22 Mar 2017 - 23:21

score 272 · Answer 6 · 2017-03-24 14:16:51

272

Views

$\phi \mapsto \lim_{\epsilon \to 0} \int_{\mathbb{R}^n} \frac{\phi (x)}{\left \Vert x \right \Vert-1 + i\epsilon}$ is a distribution

Published on 24 Mar 2017 - 14:16

score 576 · Answer 7 · 2017-04-04 05:04:37

576

Views

Hilbert-valued Schwartz functions

Published on 04 Apr 2017 - 5:04

score 479 · Answer 8 · 2017-04-07 12:56:57

479

Views

Order of antiderivatives of Schwartz functions

Published on 07 Apr 2017 - 12:56

score 68 · Answer 9 · 2023-01-30 14:54:04

68

Views

Show that $ T_f(\varphi):=\int f \varphi d x, \quad \varphi \in \mathcal{S} $ is a tempered distribution.

Published on 30 Jan 2023 - 14:54

score 75 · Answer 10 · 2023-02-01 00:51:35

75

Views

Showing Boundedness of Linear Operator on Schwartz Space

Published on 01 Feb 2023 - 0:51

score 57 · Answer 11 · 2023-02-05 21:57:32

57

Views

Exact definition of Fourier transform on L^p and some calculation

Published on 05 Feb 2023 - 21:57

score 45 · Answer 12 · 2023-02-06 10:11:11

45

Views

If $\varphi\in\mathcal{S}(\mathbb{R}):\int_\mathbb{R}\varphi dx=1$, does it then follow that $\sum_{k}\hat{\varphi}(k) \leq 2$?

Published on 06 Feb 2023 - 10:11

score 197 · Answer 13 · 2026-03-26 06:33:38

197

Views

Can Schwartz class functions be nowhere analytic?

Published on 26 Mar 2026 - 6:33

score 110 · Answer 14 · 2023-02-26 17:40:32

110

Views

Analytic continuation of $I(s)=\frac{1}{\Gamma(s)}\int^\infty_0 f(x)x^{s-1}\, dx$

Published on 26 Feb 2023 - 17:40

score 47 · Answer 15 · 2023-03-02 12:35:31

47

Views

difference between $H_s^0(\mathbb{R}^n)$ and $ H_s(\mathbb{R}^n)$

Published on 02 Mar 2023 - 12:35

List Question

Changing order of integration in the Fourier inversion formula for the Schwartz functions

If each $f_n$ is radial Schwartz, and $\|f_n\|_{L^{\infty}} \geq 1,$ can we choose $\{x_n\}$ bounded with $|f_n(x_n)|\geq 1$?

Given a Schwartz function, is it always possible to write it as a product of two Schwartz function?

Is this a tempered distribution?

Is $\frac{1}{H(x) \pm i0}$ a distribution if $|\nabla H| \neq 0$ for $H(x)=0$?

$\phi \mapsto \lim_{\epsilon \to 0} \int_{\mathbb{R}^n} \frac{\phi (x)}{\left \Vert x \right \Vert-1 + i\epsilon}$ is a distribution

Hilbert-valued Schwartz functions

Order of antiderivatives of Schwartz functions

Show that $ T_f(\varphi):=\int f \varphi d x, \quad \varphi \in \mathcal{S} $ is a tempered distribution.

Showing Boundedness of Linear Operator on Schwartz Space

Exact definition of Fourier transform on L^p and some calculation

If $\varphi\in\mathcal{S}(\mathbb{R}):\int_\mathbb{R}\varphi dx=1$, does it then follow that $\sum_{k}\hat{\varphi}(k) \leq 2$?

Can Schwartz class functions be nowhere analytic?

Analytic continuation of $I(s)=\frac{1}{\Gamma(s)}\int^\infty_0 f(x)x^{s-1}\, dx$

difference between $H_s^0(\mathbb{R}^n)$ and $ H_s(\mathbb{R}^n)$

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