List questions from schwartz-space

Published on 22 Dec 2020 - 19:46

65

Views

If $f$ is Schwartz, does $f=\mathcal{O}\left(e^{-a|x|^{\epsilon}}\right)$ for some $a,\epsilon>0$?

Published on 14 Jan 2021 - 22:25

95

Views

Density of Schwartz functions in $L^2$ on a compact domain

Published on 22 Feb 2021 - 15:03

315

Views

About convergence in Schwartz space

Published on 22 Feb 2021 - 23:02

114

Views

Does a dense subspace of test functions induce the (weak-$\ast$) topology on the space of distributions?

Published on 24 Feb 2021 - 11:30

146

Views

Show that the finite part of $\frac{1}{x_+}$ is a distribution

Published on 05 Mar 2021 - 18:23

222

Views

If $\phi$ is in $\mathcal S$ and $\phi(0)=0$, is $\int_0^1 \nabla \phi(tx)dt$ in $\mathcal S$ too?

Published on 19 Mar 2021 - 11:50

25

Views

Does $fT_n \to fT$ for a Schwartz Function and Tempered Distribution?

Published on 22 Mar 2021 - 0:45

917

Views

Hilbert transform of Schwartz function is in $L^1$ iff $\int_{\mathbb R} f=0$

Published on 26 Mar 2021 - 8:19

122

Views

When a distribution on $\mathbb{R}^n$ is smooth of compact support

Published on 31 Mar 2021 - 15:39

316

Views

Uniform convergence and Schwartz space

Published on 15 Apr 2021 - 16:27

43

Views

Regarding a property of Schwartz class.

Published on 16 Apr 2021 - 5:24

828

Views

Bound $L^1$-norm of Schwartz function using fourier transform

Published on 18 Apr 2021 - 13:01

218

Views

Generalized form of the Bernstein inequality

Published on 20 Apr 2021 - 1:21

123

Views

Show that $0$ is the only distribution solution of $u''-u=0$ in $\mathcal{S}'(\mathbb{R})$

Published on 29 Apr 2021 - 17:56

List Question

Exchanging limit and integral

If $f$ is Schwartz, does $f=\mathcal{O}\left(e^{-a|x|^{\epsilon}}\right)$ for some $a,\epsilon>0$?

Density of Schwartz functions in $L^2$ on a compact domain

About convergence in Schwartz space

Does a dense subspace of test functions induce the (weak-$\ast$) topology on the space of distributions?

Show that the finite part of $\frac{1}{x_+}$ is a distribution

If $\phi$ is in $\mathcal S$ and $\phi(0)=0$, is $\int_0^1 \nabla \phi(tx)dt$ in $\mathcal S$ too?

Does $fT_n \to fT$ for a Schwartz Function and Tempered Distribution?

Hilbert transform of Schwartz function is in $L^1$ iff $\int_{\mathbb R} f=0$

When a distribution on $\mathbb{R}^n$ is smooth of compact support

Uniform convergence and Schwartz space

Regarding a property of Schwartz class.

Bound $L^1$-norm of Schwartz function using fourier transform

Generalized form of the Bernstein inequality

Show that $0$ is the only distribution solution of $u''-u=0$ in $\mathcal{S}'(\mathbb{R})$

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