Diophantine tori and spectral asymptotics for non-selfadjoint operators

Details Diophantine tori and spectral asymptotics for non-selfadjoint operators Diophantine tori and spectral asymptotics for non-selfadjoint operators

2005-02-01

arxiv.org/abs/math/0502032v1

Mathematics

Spectral Theory

81 pages

Scientific paper

We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori enjoying a Diophantine property. We get complete asymptotic expansions for all eigenvalues in certain rectangles in the complex plane in two different cases: in the first case, we assume that the strength $\epsilon$ of the perturbation is ${\cal O}(h^{\delta})$ for some $\delta>0$ and is bounded from below by a fixed positive power of $h$. In the second case, $\epsilon$ is assumed to be sufficiently small but independent of $h$, and we describe the eigenvalues completely in a fixed $h$-independent domain in the complex spectral plane.

Affiliated with

Also associated with

No associations

Rating

Diophantine tori and spectral asymptotics for non-selfadjoint operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Diophantine tori and spectral asymptotics for non-selfadjoint operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diophantine tori and spectral asymptotics for non-selfadjoint operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-61168