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Results tagged with sp.spectral-theory
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user 19325
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
7
votes
1
answer
349
views
Eigenfunctions restricted on closed geodesics
Consider the flat torus $T^2=\frac{\mathbb{R}^2}{l_1\mathbb{Z}\oplus l_2\mathbb{Z}}$. It is easy to see that the eigenvalues of the Laplacian on torus, $-\frac{\partial^2}{\partial x^2}-\frac{\partial …
4
votes
1
answer
316
views
Functional equations for spectral zeta function
Functional equation in the theory of zeta functions is one of the important components of this theory.
I am interested to know whether the similar property, having functional equation, for the spec …
19
votes
4
answers
899
views
Has Witten's perturbation on de Rham complex been studied on other elliptic complexes?
In his famous work, Supersymmetry and Morse theory, Witten perturbs de Rham complex by perturbing the exterior derivative
$$d_h=e^{-ht}de^{ht}.$$
And he proves Morse inequality using some spectral inf …