Tagged Questions
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1answer
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Orthonormal basis in Hilbert spaces
I have a general question but I'm going got ask it in a very restrictive setup.
It is known that an equivalent condition for a system $\left\{e^{i\lambda t}\right\} _{\lambda\in\Lambda}$ being an ONB ...
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1answer
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Canonical field of Hilbert spaces in Dixmier; Plancherel Theorem
I'm working through the proof of Plancherel's Theorem in $C^{*}$-algebras by Dixmier, section 18.8. For the most part, I'm happy with it, although I have one problem. From Dixmier, I have the proof ...
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1answer
134 views
On the regularity of the Laplace equations and tensor products and such
To start with, let me apologize for my ignorance as I know next to nothing about partial differential equations. My question is about the tensor product of Banach spaces but actually I do not ...
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3answers
157 views
Why is it useful to express PDE solutions as $L^2$-convergent series?
The existence of an $L^2$ orthonormal basis consisting of eigenfunctions of a Sturm-Liouville equation helps us to express the solutions of various ODEs and PDEs as infinite series. However, in the ...
