TY - JOUR

T1 - Resonance theory for perturbed Hill operator

AU - Korotyaev, E.

PY - 2011

Y1 - 2011

N2 - We consider the Schr\"odinger operator H with a periodic potential p plus a compactly supported potential q on the real line. The spectrum of H consists of an absolutely continuous part plus a finite number of simple eigenvalues below the spectrum and in each open spectral gap . We prove the following results: 1) the distribution of resonances in the disk with large radius is determined, 2) the asymptotics of eigenvalues and antibound states are determined at high energy gaps.

AB - We consider the Schr\"odinger operator H with a periodic potential p plus a compactly supported potential q on the real line. The spectrum of H consists of an absolutely continuous part plus a finite number of simple eigenvalues below the spectrum and in each open spectral gap . We prove the following results: 1) the distribution of resonances in the disk with large radius is determined, 2) the asymptotics of eigenvalues and antibound states are determined at high energy gaps.

KW - resonances

KW - S-matrix

U2 - DOI: 10.3233/ASY-2011-1050

DO - DOI: 10.3233/ASY-2011-1050

M3 - статья

VL - 74

SP - 199

EP - 227

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -