Question

Show that for any $f\in L^1$ and $g \in L^p(\mathbb R)$, $\lVert f ∗ g\rVert_p \leqslant \lVert f\rVert_1\lVert g\rVert_p$.

score 1.2k · Answer 1 · 2014-01-16 16:44:16

1.2k

Views

Show that for any $f\in L^1$ and $g \in L^p(\mathbb R)$, $\lVert f ∗ g\rVert_p \leqslant \lVert f\rVert_1\lVert g\rVert_p$.

Published on 16 Jan 2014 - 16:44

score 247 · Answer 2 · 2014-01-16 21:25:07

247

Views

Proof of convolution inequality

Published on 16 Jan 2014 - 21:25

score 2k · Answer 3 · 2014-01-20 10:23:56

2k

Views

$f$ is bounded and continious $\Rightarrow$ the convolution integral $\int f(\tau)g(x-\tau)\text{ d}\tau$ is bounded and continuous

Published on 20 Jan 2014 - 10:23

score 1.4k · Answer 4 · 2014-01-24 01:08:47

1.4k

Views

Evaluating the convolution integral of two sine functions

Published on 24 Jan 2014 - 1:08

score 199 · Answer 5 · 2014-01-26 21:30:28

199

Views

Third Moment of a Sum of Normal and Gamma

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score 334 · Answer 6 · 2014-01-29 23:53:27

334

Views

Hölder's inequality. Understanding proof?!

Published on 29 Jan 2014 - 23:53

score 145 · Answer 7 · 2014-01-30 20:47:18

145

Views

Sums of random variables expressed as convolution

Published on 30 Jan 2014 - 20:47

score 212 · Answer 8 · 2026-03-26 10:56:32

212

Views

Is convolution associative with regards to the complex unity?

Published on 26 Mar 2026 - 10:56

score 109 · Answer 9 · 2014-02-01 19:49:26

109

Views

Asymptotics of a convolution

Published on 01 Feb 2014 - 19:49

score 113 · Answer 10 · 2014-02-02 11:35:31

113

Views

Sums of normal CDF's

Published on 02 Feb 2014 - 11:35

score 1.1k · Answer 11 · 2026-02-25 01:51:54

1.1k

Views

Differentiating a convolution integral

Published on 25 Feb 2026 - 1:51

score 1.9k · Answer 12 · 2026-04-02 18:35:30

1.9k

Views

Dirac delta convolution with function

Published on 02 Apr 2026 - 18:35

score 1.5k · Answer 13 · 2014-02-04 21:38:32

1.5k

Views

Is the convolution of a function $f(x)$ and a polynomial $p(x)$ always a polynomial?

Published on 04 Feb 2014 - 21:38

score 429 · Answer 14 · 2014-02-11 18:50:13

429

Views

Convolution of a product with focal kernel

Published on 11 Feb 2014 - 18:50

score 128 · Answer 15 · 2014-02-12 22:00:03

128

Views

What is the solution of this differential equation? / How to solve it?

Published on 12 Feb 2014 - 22:00

List Question

Show that for any $f\in L^1$ and $g \in L^p(\mathbb R)$, $\lVert f ∗ g\rVert_p \leqslant \lVert f\rVert_1\lVert g\rVert_p$.

Proof of convolution inequality

$f$ is bounded and continious $\Rightarrow$ the convolution integral $\int f(\tau)g(x-\tau)\text{ d}\tau$ is bounded and continuous

Evaluating the convolution integral of two sine functions

Third Moment of a Sum of Normal and Gamma

Hölder's inequality. Understanding proof?!

Sums of random variables expressed as convolution

Is convolution associative with regards to the complex unity?

Asymptotics of a convolution

Sums of normal CDF's

Differentiating a convolution integral

Dirac delta convolution with function

Is the convolution of a function $f(x)$ and a polynomial $p(x)$ always a polynomial?

Convolution of a product with focal kernel

What is the solution of this differential equation? / How to solve it?

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