List questions from distribution-theory

Published on 12 Apr 2026 - 16:59

697

Views

2D Dirac delta function: how to prove $\delta(ax, by) = \frac{1}{|ab|} \delta(x,y)$?

Published on 08 Apr 2026 - 18:01

62

Views

What is the integral of this expression in the sense of distribution?

Published on 12 Apr 2026 - 6:51

44

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Primitive of Cauchy Principal Value?

Published on 26 Mar 2026 - 14:42

72

Views

Integral involving derivative of delta function

Published on 10 Apr 2026 - 6:36

34

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Show that $\mu_{f+g}(\lambda_1+\lambda_2) \le \mu_f(\lambda_1)+\mu_g(\lambda_2)$ for $\lambda_1, \lambda_2 \ge 0$

Published on 01 Apr 2026 - 10:22

75

Views

Structure/Order of explaining distribution-theory

Published on 26 Mar 2026 - 2:41

45

Views

How to prove that $(\tau^v)^* = \tau^{-v}$ for distributions?

Published on 11 Apr 2026 - 7:06

44

Views

An application of the sequential continuity of convolution of distributions

Published on 19 Oct 2021 - 10:51

66

Views

Smoothness of a distribution

Published on 12 Apr 2026 - 11:14

54

Views

Definition of convolution for $u \in \mathcal{E}'(\mathbb{R}^n)$ and $\varphi \in C^{\infty}(\mathbb{R}^n).$

Published on 12 Apr 2026 - 8:19

89

Views

On fourier transform of convolution

Published on 12 Apr 2026 - 6:30

40

Views

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

Published on 09 Apr 2026 - 5:47

209

Views

Transition density of Brownian motion killed at $\partial D$

Published on 11 Apr 2026 - 22:08

97

Views

Verifying that a function lives in $H^{-1}(D)$

Published on 30 Mar 2026 - 16:59

List Question

Find weak derivative of sign-like function

2D Dirac delta function: how to prove $\delta(ax, by) = \frac{1}{|ab|} \delta(x,y)$?

What is the integral of this expression in the sense of distribution?

Primitive of Cauchy Principal Value?

Integral involving derivative of delta function

Show that $\mu_{f+g}(\lambda_1+\lambda_2) \le \mu_f(\lambda_1)+\mu_g(\lambda_2)$ for $\lambda_1, \lambda_2 \ge 0$

Structure/Order of explaining distribution-theory

How to prove that $(\tau^v)^* = \tau^{-v}$ for distributions?

An application of the sequential continuity of convolution of distributions

Smoothness of a distribution

Definition of convolution for $u \in \mathcal{E}'(\mathbb{R}^n)$ and $\varphi \in C^{\infty}(\mathbb{R}^n).$

On fourier transform of convolution

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

Transition density of Brownian motion killed at $\partial D$

Verifying that a function lives in $H^{-1}(D)$

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