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Results tagged with sp.spectral-theory
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user 20729
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
37
votes
Can you hear the shape of a drum by choosing where to drum it?
Sometimes you can
Since there seem to be no hard results along these lines on the literature, I decided to have a look at the two shapes in the question and see if there are some relatively accessibl …
- 2,358
74
votes
2
answers
3k
views
Can you hear the shape of a drum by choosing where to drum it?
I find the problem of hearing the shape of a drum fascinating. Specifically, given two connected subsets of $\mathbb R^2$ with piecewise-smooth boundaries (or a suitable generalization to a riemannian …
- 2,358
0
votes
Conditions ensuring an order betweenthe smallest eigenvalues of two positive definite Jacob...
Felix is correct in the small $b$ limit. In the very large $b$ limit, on the other hand, the spectra of $J$ and $L$ will coincide, so one needs some more finesse. The following is a rough, approximate …