Resonances for steplike potentials: Forward and inverse results

被引：21

作者：

Christiansen, T ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 358卷 / 05期

关键词：

steplike potentials; Schrodinger operator; resonances; inverse problem;

D O I：

10.1090/S0002-9947-05-03716-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider resonances associated to the one dimensional Schrodinger operator - (d2)/(dx2) + V ( x), where V ( x) = V+ if x > x(M) and V ( x) = V- if x < -x(M), with V+ not equal V-. We obtain asymptotics of the resonance-counting function for several regions. Moreover, we show that in several situations, the resonances, V+, and V- determine V uniquely up to translation.

引用

页码：2071 / 2089

页数：19

共 23 条

[1] On the inverse resonance problem [J].

Brown, BM ;

Knowles, I ;

Weikard, R .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 68 :383-401

[2] Asymptotics for a resonance-counting function for potential scattering on cylinders [J].

Christiansen, T .

JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 216 (01) :172-190

[3] Some upper bounds on the number of resonances for manifolds with infinite cylindrical ends [J].

Christiansen, T .

ANNALES HENRI POINCARE, 2002, 3 (05) :895-920

[4] SCATTERING AND INVERSE SCATTERING FOR STEPLIKE POTENTIALS IN THE SCHRODINGER-EQUATION [J].

COHEN, A ;

KAPPELER, T .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1985, 34 (01) :127-180

[5] Asymptotic distribution of resonances in one dimension [J].

Froese, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 137 (02) :251-272

[6] Upper bounds for the resonance counting function of Schrodinger operators in odd dimensions [J].

Froese, R .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1998, 50 (03) :538-546

[7]

GUILLOPE L, 1989, ANN SCI ECOLE NORM S, V22, P137

[8]

Korotyaev E, 2004, ASYMPTOTIC ANAL, V37, P215

[9]

KOROTYAEV E, INVERSE RESONANCE SC

[10]

Levin B. Ja., 1964, DISTRIBUTION ZEROS E

← 1 2 3 →