Details

Autor(en) / Beteiligte

• Shafarevich, Andrei
• Michalik, Sławomir
• Filipuk, Galina
• Lastra, Alberto

Titel

Quantization Conditions on Riemannian Surfaces and Spectral Series of Non-selfadjoint Operators

Ist Teil von

• Formal and Analytic Solutions of Diff. Equations, p.177-187

Ort / Verlag

Cham: Springer International Publishing

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In the paper, the review of the papers [26–30, 32–34] devoted to the semiclassical asymptotic behavior of the eigenvalues of some nonself-adjoint operators important for applications is given. 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, which 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), 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.