List questions from distribution-theory

Published on 13 Apr 2026 - 9:47

40

Views

Swapping order of distribution and integration

Published on 13 Apr 2026 - 8:58

167

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bounded convergence in $L^2$ and $\mathcal{D}'$

Published on 18 Mar 2022 - 17:50

67

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integral in the sense of distributions

Published on 12 Apr 2026 - 16:01

142

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How to "formally" prove that $x(t)=\frac{1}{4}(2-t)^2\theta(2-t)$ solves $\dot{x}=-\text{sgn}(x)\sqrt{|x|},\,x(0)=1$?

Published on 09 Apr 2026 - 10:03

179

Views

How can the integral of the Dirac delta be defined if its domain is the space of test functions?

Published on 10 Apr 2026 - 8:44

130

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Does $x(t) = \exp\left(\frac{t}{t-1}\right)\cdot\theta(1-t)$ solve $\dot{x}\cdot(1-t)^2+x=0,\,\,x(0)=1$?

Published on 09 Apr 2026 - 10:04

56

Views

Derivative of $f(x) := \min(H(a+x),H(b-x))$ in the sense of distributions (Schwarz)

Published on 13 Apr 2026 - 4:41

170

Views

Understanding arbitrary currents and currents of integration.

Published on 09 Apr 2026 - 2:27

47

Views

Making sense of $\int_{\mathbb{R}^3} \frac{\partial^2}{\partial y_i \partial y_j} \left( \frac{1}{|x-y|} \right) \mathrm{d}y$ using distributions

Published on 12 Apr 2026 - 16:18

93

Views

Is $r(t) = \frac{1}{144}(T-t)^4\theta(T-t)$ a valid solution to $\ddot{r}=\sqrt{r},\,r(0)=\frac{T^4}{144}>0$? (with $\theta(t)$ the Heaviside step fn)

Published on 09 Apr 2026 - 10:04

57

Views

How to prove $\tau$ is a topology in $D(\Omega)$?

Published on 10 Apr 2026 - 3:54

75

Views

Meaning of "asymptotic distribution" of estimator in Generalized Linear Models.

Published on 12 Apr 2026 - 21:49

93

Views

The condition in J.L. Lions' lemma

Published on 12 Apr 2026 - 17:33

146

Views

Find all solution of the differential equation $y^{\prime\prime} + 4y =\delta$

Published on 13 Apr 2026 - 16:54

List Question

Proving a certain distribution is a Schwartz function

Swapping order of distribution and integration

bounded convergence in $L^2$ and $\mathcal{D}'$

integral in the sense of distributions

How to "formally" prove that $x(t)=\frac{1}{4}(2-t)^2\theta(2-t)$ solves $\dot{x}=-\text{sgn}(x)\sqrt{|x|},\,x(0)=1$?

How can the integral of the Dirac delta be defined if its domain is the space of test functions?

Does $x(t) = \exp\left(\frac{t}{t-1}\right)\cdot\theta(1-t)$ solve $\dot{x}\cdot(1-t)^2+x=0,\,\,x(0)=1$?

Derivative of $f(x) := \min(H(a+x),H(b-x))$ in the sense of distributions (Schwarz)

Understanding arbitrary currents and currents of integration.

Making sense of $\int_{\mathbb{R}^3} \frac{\partial^2}{\partial y_i \partial y_j} \left( \frac{1}{|x-y|} \right) \mathrm{d}y$ using distributions

Is $r(t) = \frac{1}{144}(T-t)^4\theta(T-t)$ a valid solution to $\ddot{r}=\sqrt{r},\,r(0)=\frac{T^4}{144}>0$? (with $\theta(t)$ the Heaviside step fn)

How to prove $\tau$ is a topology in $D(\Omega)$?

Meaning of "asymptotic distribution" of estimator in Generalized Linear Models.

The condition in J.L. Lions' lemma

Find all solution of the differential equation $y^{\prime\prime} + 4y =\delta$

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