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Results tagged with sp.spectral-theory
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user 7294
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
6
votes
3
answers
245
views
Stability of the spectrum for perturbations of the boundary
Consider the Laplace operator on a smooth bounded open set with Dirichlet boundary conditions. I need some result of the following type: if one perturbs the boundary in a suitable sense to be determin …
- 9,007
10
votes
4
answers
775
views
Does a quantitative version of Fredholm theory exist?
Let $X$ be a Banach space and $K:X\to X$ be a compact operator. If $I+K$ is injective then it is onto and hence the inverse $(I+K)^{-1}$ is bounded. What kind of qualitative or quantitative assumption …
- 9,007
3
votes
0
answers
91
views
The numerical range of a composition of two operators
For a problem I'm working on, I need the following implication. $A,B$ are two closed densely defined operators on a Hilbert space $H$. I'll be a bit vague about the setting, add assumptions at will as …
- 9,007
17
votes
4
answers
2k
views
An experiment on random matrices
A bit unsure if my use/mention of proprietary software might be inappropriate or even frowned upon here. If this is the case, or if this kind of experimental question is not welcome, please let me kno …
- 9,007
9
votes
1
answer
705
views
Counterexamples to weak dispersion for the Schrödinger group
Let $A$ be a selfadjoint operator on some Hilbert space $H$, let $U(t)=e^{itA}$ be the corresponding continuous group, and let $f\in H$ be orthogonal to all eigenvectors of $A$. Are there examples suc …
- 9,007
23
votes
3
answers
3k
views
Trapped rays bouncing between two convex bodies
At some point during my research I was confronted with this problem, but I did not dedicate serious time to it. Anyway it stayed in the back of my mind and I'm still interested in hints for it. Applic …
- 9,007