semiclassical asymptotics of eigenvalues for non-selfadjoint operators and quantization conditions on riemann surfaces

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ID: 191784
2014
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Abstract
This paper reports a study of the semiclassical asymptotic behavior of the eigenvalues of some nonself-adjoint operators that are important for applications. These operators are the Schrödinger operator with complex periodic potential and the operator of induction. It turns out that the asymptotics of the spectrum can be calculated using the quantization conditions. These can be represented as the condition that the integrals of a holomorphic form over the cycles on the corresponding complex Lagrangian manifold, which is a Riemann surface of constant energy, are integers. In contrast to the real case (the Bohr–Sommerfeld–Maslov formulas), in order to calculate a chosen spectral series, it is sufficient to assume that the integral over only one of the cycles takes integer values, and different cycles determine different parts of the spectrum.
Reference Key
esina2014actasemiclassical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Anna I. Esina;Andrei I. Shafarevich
Journal the journal of nutrition
Year 2014
DOI
10.14311/AP.2014.54.0101
URL
https://ojs.cvut.cz/ojs/index.php/ap/article/view/2077
Keywords
engineering (general) civil engineering (general)

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