Question

$|g(t_{1}) e^{-(t_{1}-x)^{2}}- g(t_{2})e^{-(t_{2}-x)^{2}}|\leq |f(t_{1}) e^{-(t_{1}-x)^{2}}- f(t_{2})e^{-(t_{2}-x)^{2}}| $?

score 31 · Answer 1 · 2014-05-08 16:23:17

31

Views

$|g(t_{1}) e^{-(t_{1}-x)^{2}}- g(t_{2})e^{-(t_{2}-x)^{2}}|\leq |f(t_{1}) e^{-(t_{1}-x)^{2}}- f(t_{2})e^{-(t_{2}-x)^{2}}| $?

Published on 08 May 2014 - 16:23

score 103 · Answer 2 · 2014-05-17 13:38:38

103

Views

Exists $C$ constant: $||f||_{L^{\infty}(\mathbb{R})}\leq\{ ||f||_{L^2(\mathbb{R}}+||f'||_{L^2(\mathbb{R})} \}, \forall f\in S(\mathbb{R})$

Published on 17 May 2014 - 13:38

score 112 · Answer 3 · 2014-05-26 11:21:32

112

Views

Do we have $C^\infty \cap \mathcal{O}_C' = \mathcal{S}$ and/or $C^\infty \cap \mathcal{S}' = \mathcal{O}_M$?

Published on 26 May 2014 - 11:21

score 2.1k · Answer 4 · 2014-05-31 10:07:19

2.1k

Views

Integration of a function in Schwartz space

Published on 31 May 2014 - 10:07

score 1.1k · Answer 5 · 2014-06-27 15:49:51

1.1k

Views

Show that $e^{-a|x|}$ does not belong to Schwartz space

Published on 27 Jun 2014 - 15:49

score 66 · Answer 6 · 2014-07-06 07:23:55

66

Views

Does there exists $f\in \mathcal{S} (\mathbb R)$ so $\hat{f}=1$ on a comapct set $C$ and $\hat{f}=0$ outside $C\subset W$ (open set)?

Published on 06 Jul 2014 - 7:23

score 105 · Answer 7 · 2014-07-09 14:08:30

105

Views

If $\phi\in \mathcal{S}(\mathbb R) $ then $\phi_{t}(x)=\frac{1}{t} \phi(x/t)\in\mathcal{S}(\mathbb R)$?

Published on 09 Jul 2014 - 14:08

score 107 · Answer 8 · 2014-07-17 18:43:34

107

Views

Characterization of $\mathscr{S}(\mathbb R^n)$?

Published on 17 Jul 2014 - 18:43

score 68 · Answer 9 · 2014-07-21 11:41:43

68

Views

How to choose, $\phi \in C^{\infty}_{c}(\mathbb R)$ such that its Fourier transform $\hat{\phi}$ is 1 in some neighbourhood of the given point?

Published on 21 Jul 2014 - 11:41

score 4.3k · Answer 10 · 2014-07-21 23:52:35

4.3k

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score 154 · Answer 11 · 2026-03-25 17:45:27

154

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score 113 · Answer 12 · 2014-08-26 16:12:27

113

Views

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score 173 · Answer 13 · 2014-10-04 15:11:06

173

Views

Showing that the quotient of a function belonging to Schwartz Space by a strictly positive polynomial remains in the Schwartz Space

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score 25 · Answer 14 · 2014-10-19 15:29:28

25

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score 2.8k · Answer 15 · 2014-10-24 22:43:43

2.8k

Views

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Published on 24 Oct 2014 - 22:43

List Question

$|g(t_{1}) e^{-(t_{1}-x)^{2}}- g(t_{2})e^{-(t_{2}-x)^{2}}|\leq |f(t_{1}) e^{-(t_{1}-x)^{2}}- f(t_{2})e^{-(t_{2}-x)^{2}}| $?

Exists $C$ constant: $||f||_{L^{\infty}(\mathbb{R})}\leq\{ ||f||_{L^2(\mathbb{R}}+||f'||_{L^2(\mathbb{R})} \}, \forall f\in S(\mathbb{R})$

Do we have $C^\infty \cap \mathcal{O}_C' = \mathcal{S}$ and/or $C^\infty \cap \mathcal{S}' = \mathcal{O}_M$?

Integration of a function in Schwartz space

Show that $e^{-a|x|}$ does not belong to Schwartz space

Does there exists $f\in \mathcal{S} (\mathbb R)$ so $\hat{f}=1$ on a comapct set $C$ and $\hat{f}=0$ outside $C\subset W$ (open set)?

If $\phi\in \mathcal{S}(\mathbb R) $ then $\phi_{t}(x)=\frac{1}{t} \phi(x/t)\in\mathcal{S}(\mathbb R)$?

Characterization of $\mathscr{S}(\mathbb R^n)$?

How to choose, $\phi \in C^{\infty}_{c}(\mathbb R)$ such that its Fourier transform $\hat{\phi}$ is 1 in some neighbourhood of the given point?

Rapidly Decreasing Functions

Nuclearity of $\mathscr{S}$

Understanding this characterization of Schwartz's space

Showing that the quotient of a function belonging to Schwartz Space by a strictly positive polynomial remains in the Schwartz Space

Giving a bound for |f(x) \star \phi_k(x) -f(x)|

Formal proof that Schwartz space is space of rapidly decreasing functions

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