List questions from convolution

Published on 03 Apr 2026 - 21:27

39

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How to show $x_+^{a-1} * x_+^{b-1}=B(a,b)x_+^{a+b-1}$

Published on 22 Oct 2021 - 20:17

88

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Fubini's theorem with unbounded but summable integrand

Published on 23 Mar 2026 - 5:17

19

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Confusion in step for deriving convolution formula

Published on 24 Mar 2026 - 12:34

57

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$F*f$ is absolutely continuous in $\mathbb{R}$

Published on 24 Feb 2026 - 9:50

132

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Inverse Fourier transform of a function multiplied by $x$

Published on 27 Oct 2021 - 7:47

143

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Can I join smoothly (and convexly) two pieces of function?

Published on 04 Apr 2026 - 3:52

24

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For any probability density function f, does it always exists another probability g such that f = g∗g? (* means convolution)

Published on 06 Apr 2026 - 11:14

50

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Laplace transform of $y(t)$

Published on 04 Nov 2021 - 5:47

43

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What is the gradient operator in this context?

Published on 25 Mar 2026 - 11:09

55

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$S$ a distribution with compact support, $\phi \in \mathcal{C}^{\infty}_{c}$ then :$y\mapsto\langle S,\phi(.+y)\rangle\in\mathcal{C}^{\infty}_{c}$

Published on 05 Nov 2021 - 19:20

182

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Convolution of an $L^2$ function with an $L^1$ function converges

Published on 06 Nov 2021 - 20:36

30

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Validity of convolution theorems

Published on 08 Nov 2021 - 14:12

2.2k

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Inverse convolution theorem: $ \mathcal{F}^{-1}(f*g)(t) = \mathcal{F}^{-1}{f}(t)\mathcal{F}^{-1}{g}(t)$

Published on 10 Nov 2021 - 17:51

223

Views

Compactness of convolution operator

Published on 25 Mar 2026 - 15:37

List Question

Given product and convolution of pair of functions can you find original pair?

How to show $x_+^{a-1} * x_+^{b-1}=B(a,b)x_+^{a+b-1}$

Fubini's theorem with unbounded but summable integrand

Confusion in step for deriving convolution formula

$F*f$ is absolutely continuous in $\mathbb{R}$

Inverse Fourier transform of a function multiplied by $x$

Can I join smoothly (and convexly) two pieces of function?

For any probability density function f, does it always exists another probability g such that f = g∗g? (* means convolution)

Laplace transform of $y(t)$

What is the gradient operator in this context?

$S$ a distribution with compact support, $\phi \in \mathcal{C}^{\infty}_{c}$ then :$y\mapsto\langle S,\phi(.+y)\rangle\in\mathcal{C}^{\infty}_{c}$

Convolution of an $L^2$ function with an $L^1$ function converges

Validity of convolution theorems

Inverse convolution theorem: $ \mathcal{F}^{-1}(f*g)(t) = \mathcal{F}^{-1}{f}(t)\mathcal{F}^{-1}{g}(t)$

Compactness of convolution operator

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