List questions from microlocal-analysis

37

Views

Show that the convolution $u\ast\psi$ between compactly supported tempered distribution $u$ and Schwartz function $\psi$ is a test function

Published on 25 Mar 2026 - 15:58

55

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‘Positive’ commutator argument to control norms of a distributions

Published on 25 Mar 2026 - 19:05

92

Views

Inequality involving the imaginary part of a Hermitian inner product

Published on 16 Apr 2026 - 10:02

88

Views

Convergence in $\mathcal{D}'(\mathbb{R})$ via stationary phase method

Published on 25 Mar 2026 - 15:58

47

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Local injectivity of bicharacteristic curves

Published on 25 Mar 2026 - 16:01

125

Views

Wavefront set of a smooth function

Published on 05 Apr 2026 - 23:37

117

Views

Resolvent estimate of hyperbolic Laplacian

Published on 25 Mar 2026 - 17:37

450

Views

Non-compactness of the resolvent

Published on 06 Apr 2026 - 1:07

160

Views

References for microlocal versions of some theorems

Published on 25 Mar 2026 - 15:59

419

Views

wave front set - directions of singularities

Published on 25 Mar 2026 - 17:43

258

Views

Characteristic Variety of the Principal Symbol solves PDE system?

Published on 20 Apr 2026 - 12:19

333

Views

Show that a regularizing operator $K : C_c(\Omega) \to \mathcal{D}'(\Omega)$ has kernel $k \in C^\infty(\Omega \times \Omega)$.

Published on 17 Apr 2026 - 19:55

97

Views

Continuity of smoothing operators

Published on 29 Apr 2026 - 0:07

1.1k

Views

Textbook/monograph for microlocal analysis

Published on 30 Apr 2026 - 10:58

1.4k

Views

Composition of pseudo-differential operators

Published on 06 Apr 2026 - 1:25

List Question

Show that the convolution $u\ast\psi$ between compactly supported tempered distribution $u$ and Schwartz function $\psi$ is a test function

‘Positive’ commutator argument to control norms of a distributions

Inequality involving the imaginary part of a Hermitian inner product

Convergence in $\mathcal{D}'(\mathbb{R})$ via stationary phase method

Local injectivity of bicharacteristic curves

Wavefront set of a smooth function

Resolvent estimate of hyperbolic Laplacian

Non-compactness of the resolvent

References for microlocal versions of some theorems

wave front set - directions of singularities

Characteristic Variety of the Principal Symbol solves PDE system?

Show that a regularizing operator $K : C_c(\Omega) \to \mathcal{D}'(\Omega)$ has kernel $k \in C^\infty(\Omega \times \Omega)$.

Continuity of smoothing operators

Textbook/monograph for microlocal analysis

Composition of pseudo-differential operators

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