All Questions
Tagged with hilbert-spaces sp.spectral-theory
55 questions
2
votes
1
answer
541
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Does spectral theory assume separability
On an infinite dimensional space, the spectral theorem for compact normal operators says that the eigenvectors form an orthonormal basis which, from wikipedia, is equivalent to the space being ...
- 60.5k
8
votes
1
answer
844
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A doubt about the parts of the spectrum of tensor products
Let $\mathcal{H}$ be any complex Hilbert space of infinite dimensional. By an operator $T$ I mean a linear bounded transformation from $\mathcal{H}$ into $\mathcal{H}$, i.e, $T:\mathcal{H}\rightarrow\...
- 4,729
1
vote
1
answer
213
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Weyl asymptotics vs. form perturbations
Consider Hilbert spaces $V$,$H$; a closed quadratic form $a$ with domain $V$; and its associated operator $A$ on $H$. (If necessary, the form can be assumed to be coercive.) For the sake of simplicity,...
- 3,343
3
votes
1
answer
588
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orthonormal basis of eigenvectors for laplacian on a concave polygon
I am interested in the Laplace operator $\Delta$ on a concave polygon.
When the polygon is convex, it is known that $\Delta: H^2(\Omega) \rightarrow L^2(\Omega)$
is boundedly invertible. In addition, ...
- 3,343
3
votes
3
answers
3k
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Infinite hermitian matrix
Suppose we have a finite square n x n matrix of complex numbers H that is Hermitian and skew-symmetric:
$H^\dagger = H$ and $H^T = -H$.
(T denotes transpose, $\dagger$ denote conjugate transpose. I ...
- 1,471