List questions from self-adjoint-operators

Published on 17 Nov 2021 - 15:43

103

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Diffusion-Reaction problem $u_t = \int_{-\infty}^{\infty} K(x-y) u(y) dy . u + u^3$.

Published on 21 Nov 2021 - 11:16

68

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$\|T\| \leq\|T\|_{0}^{1 / 2}\left\|T^{*}\right\|_{0}^{1 / 2}$ for compact operators on Hilbert spaces.

Published on 21 Nov 2021 - 19:52

273

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Adjoint operator for a system of nonlinear PDEs

Published on 28 Nov 2021 - 2:28

27

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Is this a correct method for determining the domain of the adjoint?

Published on 04 Dec 2021 - 8:41

137

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Accumulation point of a discrete Spectrum

Published on 26 Mar 2026 - 1:28

33

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What is the adjoint of $e^{\alpha \psi} \partial_{x}^4 e^{-\alpha \psi}$?

Published on 18 Dec 2021 - 22:16

185

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Why does positive definite guarantee uniqueness? (Peter J Olver PDE book chapter 9)

Published on 19 Dec 2021 - 21:31

72

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Can we apply quadratic optimization in complex inner product spaces?

Published on 21 Dec 2021 - 11:49

56

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Monotonicity of eigenvalues in gaps (self-adjoint below bounded operator)

Published on 04 Jan 2022 - 18:24

19

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disconjugacy of a self adjoint operator

Published on 06 Jan 2022 - 9:49

480

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Show $S^2 = T$ is positive definite

Published on 10 Jan 2022 - 19:43

37

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The measurable function in the Spectral Theorem can be taken in $L^p$

Published on 11 Jan 2022 - 22:08

656

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Why is the second derivative operator self-adjoint?

Published on 13 Jan 2022 - 17:50

38

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What assumptions are needed for compactness and self-adjointness?

Published on 18 Jan 2022 - 11:36

List Question

One matrix is diagnolized by orthonormal basis of another matrix

Diffusion-Reaction problem $u_t = \int_{-\infty}^{\infty} K(x-y) u(y) dy . u + u^3$.

$\|T\| \leq\|T\|_{0}^{1 / 2}\left\|T^{*}\right\|_{0}^{1 / 2}$ for compact operators on Hilbert spaces.

Adjoint operator for a system of nonlinear PDEs

Is this a correct method for determining the domain of the adjoint?

Accumulation point of a discrete Spectrum

What is the adjoint of $e^{\alpha \psi} \partial_{x}^4 e^{-\alpha \psi}$?

Why does positive definite guarantee uniqueness? (Peter J Olver PDE book chapter 9)

Can we apply quadratic optimization in complex inner product spaces?

Monotonicity of eigenvalues in gaps (self-adjoint below bounded operator)

disconjugacy of a self adjoint operator

Show $S^2 = T$ is positive definite

The measurable function in the Spectral Theorem can be taken in $L^p$

Why is the second derivative operator self-adjoint?

What assumptions are needed for compactness and self-adjointness?

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