List questions from schwartz-space

Published on 15 May 2021 - 17:37

58

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A problem regarding a generalization of Schwartz space

Published on 22 May 2021 - 16:15

154

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Can I generalize the classical Bernstein inequality?

Published on 24 May 2021 - 6:55

270

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Show that $f(x) = e^x \cos(x)$ on $\mathbb{R}$ is a tempered distribution

Published on 02 Jun 2021 - 21:51

227

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Is there a metrizable topology on tempered distributions for which sequential convergence is pointwise?

Published on 04 Jun 2021 - 13:27

48

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Is it true that $\widehat{f(x,0)}(\xi) = \widehat{f}(\xi,0)$?

Published on 14 Jun 2021 - 14:07

203

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Convolution between a Bounded Tempered Distribution and a $L^1$ function is a distribution.

Published on 18 Jun 2021 - 1:57

141

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Fourier transform in Schwartz space

Published on 18 Jun 2021 - 13:35

327

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Grafakos, Modern Fourier Analysis, Third Edition, Exercise 2.1.4. Bounded Tempered Distributions

Published on 18 Jun 2021 - 20:56

193

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If $\langle u(t), \phi \rangle \in L^1\ \forall \phi \in S(\Bbb R^d)$, does $\langle u(t), \phi(t) \rangle \in L^1\ \forall \phi \in S(\Bbb R^{1+d})$?

Published on 25 Jun 2021 - 9:37

609

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Is the Hilbert space of quantum physics the space of tempered distributions?

Published on 02 Aug 2021 - 16:00

40

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Estimate $N_p$ norm of $\psi : x \longmapsto \int_{-\infty}^x \phi(t)\ \mathrm dt$

Published on 08 Aug 2021 - 15:53

121

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Approximate family of tempered distributions by Schwartz functions

Published on 10 Aug 2021 - 8:42

92

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A Schwartz function is measurable

Published on 26 Aug 2021 - 8:40

51

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If $f\in\mathcal{S}$, then the functions $\frac{\partial f}{\partial x_j}$ and $x_jf$ are in $\mathcal{S}$

Published on 22 Sep 2021 - 14:47

List Question

Contraction principle and ODE

A problem regarding a generalization of Schwartz space

Can I generalize the classical Bernstein inequality?

Show that $f(x) = e^x \cos(x)$ on $\mathbb{R}$ is a tempered distribution

Is there a metrizable topology on tempered distributions for which sequential convergence is pointwise?

Is it true that $\widehat{f(x,0)}(\xi) = \widehat{f}(\xi,0)$?

Convolution between a Bounded Tempered Distribution and a $L^1$ function is a distribution.

Fourier transform in Schwartz space

Grafakos, Modern Fourier Analysis, Third Edition, Exercise 2.1.4. Bounded Tempered Distributions

If $\langle u(t), \phi \rangle \in L^1\ \forall \phi \in S(\Bbb R^d)$, does $\langle u(t), \phi(t) \rangle \in L^1\ \forall \phi \in S(\Bbb R^{1+d})$?

Is the Hilbert space of quantum physics the space of tempered distributions?

Estimate $N_p$ norm of $\psi : x \longmapsto \int_{-\infty}^x \phi(t)\ \mathrm dt$

Approximate family of tempered distributions by Schwartz functions

A Schwartz function is measurable

If $f\in\mathcal{S}$, then the functions $\frac{\partial f}{\partial x_j}$ and $x_jf$ are in $\mathcal{S}$

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