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Results tagged with sp.spectral-theory
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user 15743
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
1k
views
Multiplicity of eigenvalues of the Laplacian on quaternionic projective space
Using the classic spherical harmonics theory, one obtains the $k$-th eigenvalue of the $n$-dimensional round sphere $S^n$ to be $k(k+n-1)$, and its multiplicity is $\binom{n+k}{k}-\binom{n+k-1}{k-1}$, …
- 5,891
13
votes
1
answer
2k
views
First eigenvalue of the Laplacian on Berger spheres
Consider the Hopf fibrations $S^1\to S^{2n+1}\to CP^n$ and $S^3\to S^{4n+3}\to HP^n$. These are Riemannian submersions with totally geodesic fibers. Consider now their canonical variations (the so-cal …
- 5,891
22
votes
1
answer
960
views
Avoiding integers in the spectrum of the Laplacian of a Riemann surface
Let $\Sigma^2$ be an orientable compact surface of genus $gen(\Sigma)\geq2$, and denote by $\mathcal M(\Sigma)$ the moduli space of hyperbolic metrics on $\Sigma$, i.e., Riemannian metrics of constant …
- 5,891