List questions from convolution

Published on 24 Mar 2026 - 13:55

55

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Convolution sum

Published on 19 Mar 2026 - 14:02

58

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PDF of the sum of two random variables integrates to >1

Published on 17 Mar 2026 - 20:04

84

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If $u \in \mathscr{L}^1(\lambda^n), v\in \mathscr{L}^\infty (\lambda^n)$, then $u \star v$ is bounded and continuous.

Published on 22 Mar 2026 - 4:19

547

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Proof of Young's inequality $\Vert u \star v \Vert_p \le \Vert u \Vert_1 \Vert v \Vert_p.$

Published on 20 Mar 2026 - 20:00

4.4k

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Duhamel's principle for heat equation.

Published on 22 Mar 2026 - 10:36

112

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Computing the convolution of $f(x)=\gamma1_{(\alpha,\alpha+\beta)}(x)$

Published on 19 Mar 2026 - 16:45

41

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Convolution of distributions property

Published on 20 Mar 2026 - 5:25

195

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Self-convolution of $f(\vec{r}) = e^{-x^2-y^2}/r^2$

Published on 20 Mar 2026 - 0:10

94

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Inverse $z$-transform similar to convolution

Published on 24 Mar 2026 - 11:41

194

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Convolution of rapidly decaying function with itself

Published on 20 Mar 2026 - 7:19

118

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Fourier transform of a product in two dimension

Published on 17 Mar 2026 - 10:44

41

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probability of two numbers picked from two distributions giving a fixed number multiplication

Published on 21 Mar 2026 - 21:30

43

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Show that if $\phi \in L^1(\mathbf R)$ and $f \in C_c(\mathbf R)$ then the convolution $\phi * f \in L^\infty(\mathbf R)$

Published on 23 Mar 2026 - 15:16

156

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Fourier transform of a convolution - differentiabilty

Published on 22 Mar 2026 - 20:14

List Question

What is the result of $x(at) * δ(t-k)$

Convolution sum

PDF of the sum of two random variables integrates to >1

If $u \in \mathscr{L}^1(\lambda^n), v\in \mathscr{L}^\infty (\lambda^n)$, then $u \star v$ is bounded and continuous.

Proof of Young's inequality $\Vert u \star v \Vert_p \le \Vert u \Vert_1 \Vert v \Vert_p.$

Duhamel's principle for heat equation.

Computing the convolution of $f(x)=\gamma1_{(\alpha,\alpha+\beta)}(x)$

Convolution of distributions property

Self-convolution of $f(\vec{r}) = e^{-x^2-y^2}/r^2$

Inverse $z$-transform similar to convolution

Convolution of rapidly decaying function with itself

Fourier transform of a product in two dimension

probability of two numbers picked from two distributions giving a fixed number multiplication

Show that if $\phi \in L^1(\mathbf R)$ and $f \in C_c(\mathbf R)$ then the convolution $\phi * f \in L^\infty(\mathbf R)$

Fourier transform of a convolution - differentiabilty

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