List questions from schwartz-space

Published on 13 Apr 2026 - 8:32

40

Views

A function on $\mathcal{S}(\mathbb{R}^n)$ written as a combinations of Schwartz functions

Published on 13 Apr 2026 - 14:24

25

Views

Trying to show $\mathcal S(\Bbb R)\subset L^p(\Bbb R)\ \forall 1\leq p\leq\infty$

Published on 16 Apr 2026 - 9:05

148

Views

Smooth tempered distribution

Published on 12 Apr 2026 - 7:20

1.1k

Views

Homogeneous Sobolev space and distributions

Published on 13 Apr 2026 - 22:46

119

Views

Schwartz seminorm of Fourier transform of $\phi$ bounded above by a Schwarz seminorm of $\phi$

Published on 13 Apr 2026 - 21:53

273

Views

Abuse of notation with distributions

Published on 15 Apr 2026 - 21:59

92

Views

Prove that $ \Vert (\sum_{j \in \mathbb{Z}} |\phi_{2^j} * f|^2)^{1/2}\ \Vert_p \le C\Vert f\Vert_p $

Published on 15 Apr 2026 - 10:26

191

Views

Translation invariance of distributions

Published on 10 Apr 2026 - 23:37

441

Views

Structure of tempered distribution

Published on 14 Apr 2026 - 13:22

191

Views

Use Dominated Convergence theorem in Schwartz convergent sequence

Published on 15 Apr 2026 - 6:49

672

Views

Understanding Schwartz Space / How to show a function is or is not in Schwartz Space

Published on 11 Apr 2026 - 20:00

301

Views

Applying the generalised Leibniz rule multi-index form

Published on 11 Apr 2026 - 3:08

71

Views

Fourier transformation on $\{T_\theta\}$ is surjective

Published on 11 Apr 2026 - 7:37

1.1k

Views

The convolution of functions in the Schwartz Space lies in the Schwartz Space

Published on 13 Apr 2026 - 6:10

List Question

convergence for tempered distributions

A function on $\mathcal{S}(\mathbb{R}^n)$ written as a combinations of Schwartz functions

Trying to show $\mathcal S(\Bbb R)\subset L^p(\Bbb R)\ \forall 1\leq p\leq\infty$

Smooth tempered distribution

Homogeneous Sobolev space and distributions

Schwartz seminorm of Fourier transform of $\phi$ bounded above by a Schwarz seminorm of $\phi$

Abuse of notation with distributions

Prove that $ \Vert (\sum_{j \in \mathbb{Z}} |\phi_{2^j} * f|^2)^{1/2}\ \Vert_p \le C\Vert f\Vert_p $

Translation invariance of distributions

Structure of tempered distribution

Use Dominated Convergence theorem in Schwartz convergent sequence

Understanding Schwartz Space / How to show a function is or is not in Schwartz Space

Applying the generalised Leibniz rule multi-index form

Fourier transformation on $\{T_\theta\}$ is surjective

The convolution of functions in the Schwartz Space lies in the Schwartz Space

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