Question

Given a Schwartz function $f(x,y)$ on $\mathbb{R}^{2n}$, is $f(x,x)$ necessarily a Schwartz functoin on $\mathbb{R}^n$?

score 35 · Answer 1 · 2023-12-08 11:58:15

35

Views

Given a Schwartz function $f(x,y)$ on $\mathbb{R}^{2n}$, is $f(x,x)$ necessarily a Schwartz functoin on $\mathbb{R}^n$?

Published on 08 Dec 2023 - 11:58

score 54 · Answer 2 · 2023-12-17 13:56:57

54

Views

Tempered distribution locally integrable function

Published on 17 Dec 2023 - 13:56

score 551 · Answer 3 · 2023-12-26 11:18:57

551

Views

How can tempered distributions be identified with functions?

Published on 26 Dec 2023 - 11:18

score 64 · Answer 4 · 2024-01-02 23:51:22

64

Views

Schwartz kernel theorem and musical isomorphisms

Published on 02 Jan 2024 - 23:51

score 23 · Answer 5 · 2024-01-03 10:07:26

23

Views

Proving that $\rho_\varepsilon\ast U\to U$ as $\varepsilon\to 0^+$

Published on 03 Jan 2024 - 10:07

score 77 · Answer 6 · 2024-01-03 10:25:45

77

Views

Proving that $\frac{x}{x^2+\varepsilon^2}\to \mathsf{p.v.}\left(\frac1x\right)$ in $\mathscr{S}'$

Published on 03 Jan 2024 - 10:25

score 51 · Answer 7 · 2024-01-04 17:58:39

51

Views

Confusion with identities in different function spaces

Published on 04 Jan 2024 - 17:58

score 51 · Answer 8 · 2024-02-07 19:14:11

51

Views

How to estimate schwartz space functions?

Published on 07 Feb 2024 - 19:14

score 136 · Answer 9 · 2024-02-10 17:29:01

136

Views

Paley-Wiener theorem conversion proof

Published on 10 Feb 2024 - 17:29

score 36 · Answer 10 · 2026-03-26 01:25:13

36

Views

For $f \in H^s$, then $\exists g \in C_c$ such that $f=g$ a.e.

Published on 26 Mar 2026 - 1:25

score 65 · Answer 11 · 2024-02-21 02:44:03

65

Views

Is the Schwartz space "sequentially dense" in the space of tempered dsitributions with respect to some topology?

Published on 21 Feb 2024 - 2:44

score 43 · Answer 12 · 2024-02-21 12:37:03

43

Views

Question regarding the indexes $\alpha$ and $\beta$ in the definition of Schwartz space

Published on 21 Feb 2024 - 12:37

score 26 · Answer 13 · 2024-02-21 13:00:49

26

Views

Convolution of Schwartz and $C^\infty$ function with bounded increasing

Published on 21 Feb 2024 - 13:00

score 125 · Answer 14 · 2024-02-26 08:43:38

125

Views

Is it possible to approximate any nonnegative Schwartz function by square of Schwartz functions?

Published on 26 Feb 2024 - 8:43

score 65 · Answer 15 · 2024-02-26 14:20:16

65

Views

$\sqrt{ f(x) + \alpha e^{-\lVert x \rVert^2}}$ is a Schwartz function for any nonnegative Schwartz $f$ and $\alpha>0$?

Published on 26 Feb 2024 - 14:20

List Question

Given a Schwartz function $f(x,y)$ on $\mathbb{R}^{2n}$, is $f(x,x)$ necessarily a Schwartz functoin on $\mathbb{R}^n$?

Tempered distribution locally integrable function

How can tempered distributions be identified with functions?

Schwartz kernel theorem and musical isomorphisms

Proving that $\rho_\varepsilon\ast U\to U$ as $\varepsilon\to 0^+$

Proving that $\frac{x}{x^2+\varepsilon^2}\to \mathsf{p.v.}\left(\frac1x\right)$ in $\mathscr{S}'$

Confusion with identities in different function spaces

How to estimate schwartz space functions?

Paley-Wiener theorem conversion proof

For $f \in H^s$, then $\exists g \in C_c$ such that $f=g$ a.e.

Is the Schwartz space "sequentially dense" in the space of tempered dsitributions with respect to some topology?

Question regarding the indexes $\alpha$ and $\beta$ in the definition of Schwartz space

Convolution of Schwartz and $C^\infty$ function with bounded increasing

Is it possible to approximate any nonnegative Schwartz function by square of Schwartz functions?

$\sqrt{ f(x) + \alpha e^{-\lVert x \rVert^2}}$ is a Schwartz function for any nonnegative Schwartz $f$ and $\alpha>0$?

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