List questions from distribution-theory

Published on 07 May 2016 - 18:49

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Is there a Plancherel-type identity for generalized Fourier Transforms?

Published on 08 May 2016 - 21:58

7.3k

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Second derivative of the delta function

Published on 09 May 2016 - 21:29

65

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Let $T : \mathcal{D}(\mathbb{R}) \to \mathbb{R}$ be given by $T(\phi) = |\phi(0)|$. Show that $T$ is not a distribution.

Published on 10 May 2016 - 3:35

362

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Multiplying the PV$(\frac{1}{x})$ by $x$

Published on 12 May 2016 - 2:28

301

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Obtain a tempered distribution from $1/|x|$ by subtracting a multiple of $\phi(0)$

Published on 12 May 2016 - 10:21

185

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Decomposition of complex Radon measures

Published on 01 Apr 2026 - 16:20

99

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Prove version of Bernsteins inequality $||\partial^{\alpha}f||_{L^{\infty}}\leq CR^{|\alpha|}||f||_{L^{\infty}}$

Published on 27 Mar 2026 - 2:07

380

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Space of test functions defined by norms

Published on 31 Mar 2026 - 7:50

143

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Why are these distributions positive?

Published on 26 Mar 2026 - 7:41

137

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Support of a Distribution

Published on 16 May 2016 - 22:48

122

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Fundamental Solution to 2nd Order ODE

Published on 17 May 2016 - 21:45

843

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Distributional derivative with discontinuities

Published on 18 May 2016 - 1:30

102

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Folland Exercise 9.21b

Published on 18 May 2016 - 18:22

55

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Show $supp(T_\mu) = supp(\mu)$ where $T_\mu(\phi) = \int_U \phi d\mu$ for all test functions $\phi$

Published on 19 May 2016 - 17:51

List Question

Second order differential equation with Heaviside function

Is there a Plancherel-type identity for generalized Fourier Transforms?

Second derivative of the delta function

Let $T : \mathcal{D}(\mathbb{R}) \to \mathbb{R}$ be given by $T(\phi) = |\phi(0)|$. Show that $T$ is not a distribution.

Multiplying the PV$(\frac{1}{x})$ by $x$

Obtain a tempered distribution from $1/|x|$ by subtracting a multiple of $\phi(0)$

Decomposition of complex Radon measures

Prove version of Bernsteins inequality $||\partial^{\alpha}f||_{L^{\infty}}\leq CR^{|\alpha|}||f||_{L^{\infty}}$

Space of test functions defined by norms

Why are these distributions positive?

Support of a Distribution

Fundamental Solution to 2nd Order ODE

Distributional derivative with discontinuities

Folland Exercise 9.21b

Show $supp(T_\mu) = supp(\mu)$ where $T_\mu(\phi) = \int_U \phi d\mu$ for all test functions $\phi$

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