List questions from integral-operators

Published on 05 Sep 2020 - 21:16

158

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Mercer theorem and uniformly bounded continuous function

Published on 08 Sep 2020 - 21:56

261

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Interchange Integration and Minimization

Published on 02 Oct 2020 - 13:23

24

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Positive definiteness wrt different borel measures

Published on 05 Oct 2020 - 17:18

206

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Mercer's theorem for zonal kernel

Published on 06 Oct 2020 - 18:14

133

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Dirac $\delta$-function as a limit of matrices, and eigenvalues of integral kernels.

Published on 02 Nov 2020 - 4:48

375

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Compute the spectrum of an explicit integral operator

Published on 02 Nov 2020 - 14:50

122

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How to prove that eigenfunction of translationally invariant continuous operator $ K(t-t') $ is $ \exp(iwt) $?

Published on 18 Nov 2020 - 23:12

150

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Kernel of a linear functional

Published on 31 Jan 2021 - 18:45

45

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Proving an expression for $T^n.$

Published on 13 Mar 2021 - 16:59

405

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Integration is a compact operator on $L^p([0, 1])$

Published on 23 Apr 2021 - 11:27

113

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Prove the operator $\int_0^x (x-t)f(t)dt$ is well defined.

Published on 30 May 2021 - 9:15

60

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Pullback of integral kernel operator: how to remember the formula?

Published on 08 Jun 2021 - 17:22

146

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Hilbert-Schmidt Integral Operator with Missing Eigenfunctions

Published on 18 Jun 2021 - 21:19

97

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Showing that $||K^nf||_p \leq \frac{1}{n!}||k||_\infty^n ||f||_p$ where $K$ is the integral operator coming from the kernel $k(x,y) = \max\{0,x-y\}$

Published on 19 Jun 2021 - 17:21

List Question

Example of a "weak" Compact operator

Mercer theorem and uniformly bounded continuous function

Interchange Integration and Minimization

Positive definiteness wrt different borel measures

Mercer's theorem for zonal kernel

Dirac $\delta$-function as a limit of matrices, and eigenvalues of integral kernels.

Compute the spectrum of an explicit integral operator

How to prove that eigenfunction of translationally invariant continuous operator $ K(t-t') $ is $ \exp(iwt) $?

Kernel of a linear functional

Proving an expression for $T^n.$

Integration is a compact operator on $L^p([0, 1])$

Prove the operator $\int_0^x (x-t)f(t)dt$ is well defined.

Pullback of integral kernel operator: how to remember the formula?

Hilbert-Schmidt Integral Operator with Missing Eigenfunctions

Showing that $||K^nf||_p \leq \frac{1}{n!}||k||_\infty^n ||f||_p$ where $K$ is the integral operator coming from the kernel $k(x,y) = \max\{0,x-y\}$

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