List questions from microlocal-analysis

Published on 19 Mar 2026 - 16:57

132

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Example of a Distribution where $(x, \xi) \in WF(u)$ but $(x, -\xi) \notin WF(u)$

Published on 19 Mar 2026 - 15:32

53

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Determining smooth domain for self-convolution of distribution.

Published on 19 Mar 2026 - 20:52

390

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Wavefront Set of the Heaviside Function

Published on 19 Mar 2026 - 15:04

51

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Construct $\psi \in C^\infty_0(\mathbb{R})$ so that $\psi > 0$ on $[-M,M]$ and $\partial_x (x \psi) \ge 0$

Published on 20 Mar 2026 - 1:37

32

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Show that functions $a \in C^\infty(\overline{\mathbb{B}^n})$ with $a|_{\partial{\overline{\mathbb{B}^n}}} = 0$ belong to $S^{-1}(\mathbb{R}^n)$

Published on 20 Mar 2026 - 0:03

453

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Convolution Theorem for Distributions

Published on 19 Mar 2026 - 20:20

132

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Reed and Simon definition of product of distributions

Published on 19 Mar 2026 - 21:07

117

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About FBI transform

Published on 24 Mar 2026 - 19:05

39

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Differentiation of an operator raised to a variable power

Published on 25 Mar 2026 - 5:30

57

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Product of distributions with compact support

Published on 19 Mar 2026 - 19:50

298

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Pseudo-differential operators - Motivation for definition of symbol

Published on 24 Mar 2026 - 23:46

388

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Are pseudo(micro)-local operators pseudodifferential?

Published on 25 Mar 2026 - 1:15

651

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Symbol of self-adjoint pseudodifferential operator

Published on 24 Mar 2026 - 23:44

134

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Example of pseudodifferential operators that smooth out the singularity of delta function

Published on 25 Mar 2026 - 12:37

List Question

H^s order of jump discontinuities

Example of a Distribution where $(x, \xi) \in WF(u)$ but $(x, -\xi) \notin WF(u)$

Determining smooth domain for self-convolution of distribution.

Wavefront Set of the Heaviside Function

Construct $\psi \in C^\infty_0(\mathbb{R})$ so that $\psi > 0$ on $[-M,M]$ and $\partial_x (x \psi) \ge 0$

Show that functions $a \in C^\infty(\overline{\mathbb{B}^n})$ with $a|_{\partial{\overline{\mathbb{B}^n}}} = 0$ belong to $S^{-1}(\mathbb{R}^n)$

Convolution Theorem for Distributions

Reed and Simon definition of product of distributions

About FBI transform

Differentiation of an operator raised to a variable power

Product of distributions with compact support

Pseudo-differential operators - Motivation for definition of symbol

Are pseudo(micro)-local operators pseudodifferential?

Symbol of self-adjoint pseudodifferential operator

Example of pseudodifferential operators that smooth out the singularity of delta function

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