List questions from distribution-theory

Published on 13 Jun 2020 - 15:48

69

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Convergence in $D'(\mathbb{R})$

Published on 17 Jun 2020 - 18:55

87

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If $u\in H_0^1(\Lambda,\mathbb R^2)\cap H^2(\Lambda,\mathbb R^2)$, is $\nabla^\perp\cdot\Delta u\in L^2(\Lambda)$?

Published on 26 Mar 2026 - 9:38

98

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Show that T is a regular distribution

Published on 22 Jun 2020 - 9:46

69

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Differentiating the delta function

Published on 28 Mar 2026 - 20:49

139

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Why do we need any test function to be infinitely many times differentiable?

Published on 27 Jun 2020 - 20:38

47

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What does this notation mean? (Distribution Theory)

Published on 28 Mar 2026 - 5:57

488

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Multiplying tempered distributions by smooth functions

Published on 29 Jun 2020 - 19:29

537

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$f(x) = 1 / \lvert x \rvert^2$, $x\in \mathbb{R}^3$ , for the Fourier transform F, prove by scaling: $ F(f) (y) = C \frac{1}{\lvert y\rvert}. $

Published on 02 Jul 2020 - 15:04

210

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Derivative of the delta function at some point

Published on 28 Mar 2026 - 22:26

73

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Derivative of integral defining delta function: Lost minus sign?

Published on 29 Mar 2026 - 3:10

227

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Convergence in the sense of distributions

Published on 08 Jul 2020 - 23:36

131

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Limit under integral sign for delta approximating function

Published on 12 Jul 2020 - 10:15

1.2k

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Dirac delta solutions

Published on 28 Mar 2026 - 22:24

412

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(in)equivalence of the sine and cosine representations of Dirac comb

Published on 28 Mar 2026 - 22:31

List Question

Generalized function (distribution) , measure theory and probability theory (intuition)

Convergence in $D'(\mathbb{R})$

If $u\in H_0^1(\Lambda,\mathbb R^2)\cap H^2(\Lambda,\mathbb R^2)$, is $\nabla^\perp\cdot\Delta u\in L^2(\Lambda)$?

Show that T is a regular distribution

Differentiating the delta function

Why do we need any test function to be infinitely many times differentiable?

What does this notation mean? (Distribution Theory)

Multiplying tempered distributions by smooth functions

$f(x) = 1 / \lvert x \rvert^2$, $x\in \mathbb{R}^3$ , for the Fourier transform F, prove by scaling: $ F(f) (y) = C \frac{1}{\lvert y\rvert}. $

Derivative of the delta function at some point

Derivative of integral defining delta function: Lost minus sign?

Convergence in the sense of distributions

Limit under integral sign for delta approximating function

Dirac delta solutions

(in)equivalence of the sine and cosine representations of Dirac comb

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