Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics. (English) Zbl 1032.35145

Birman, Michael; Suslina, Tatyana

Borichev, A. A. (ed.) et al., Systems, approximation, singular integral operators, and related topics. Proceedings of the 11th international workshop on operator theory and applications, IWOTA 2000, Bordeaux, France, June 13-16, 2000. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 129, 71-107 (2001).

The main goal of the authors is to give a description of the spectral characteristics of periodic differential operators (DO’s) near the threshold \(\lambda=0\). Using partial diagonalization, the authors reduce the problem to some questions of the analytic perturbation theory for the discrete spectrum. The difficulties are related to the fact that usually the unperturbed eigenvalue is multiple and the parametric is multidimensional.
For the entire collection see [Zbl 0972.00051].

Reviewer: Messoud Efendiev (Berlin)

MSC:

35P05	General topics in linear spectral theory for PDEs
47A10	Spectrum, resolvent

Keywords:

periodic differential operator; spectral theory; discrete spectrum; analytic perturbation