ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 A. Surkova, , Institute for Low Temperature Physics, Kharkov, Ukraine; A. Boutet de Monvel, Laboratoire de Physique Mathématique et Géométrie, Université Paris 7-Denis Diderot, Paris, France On the localization of the surface states for some classe of the discrete Schrödinger oparators with surface potential We consider the discrete Schrödinger operator in l^{2}(Z^{d}) whose potential is an unbounded quasiperiodic function concentrated on a subspace {0} × Z^{m} as m < d. Under the condition that the potential satisfies a certain version of the small divisors condition, it is proved that the part of the spectrum lying far enough from the spectrum of the free Laplacian is pure point, dense and has multiplicity one and the corresponding eigenfunctions decay exponentially.