Inverse scattering for impedance Schrodinger operators, I. Step-like impedance lattice

被引：1

作者：

Albeverio, S. ^{[1
,2
,3
,4
,5
,6
]}

Hryniv, R. ^{[7
]}

Mykytyuk, Ya. ^{[8
]}

机构：

[1] Univ Bonn, Inst Angew Math, Endenicher Allee 60, D-53115 Bonn, Germany

[2] HCM, SFB 611, Bonn, Germany

[3] IZKS, Bonn, Germany

[4] BiBoS, Bielefeld, Germany

[5] CERFIM, Locarno, Switzerland

[6] Univ Trento, Dip Matemat, Trento, Italy

[7] Univ Rzeszow, Dept Math & Nat Sci, 1 Pigonia Str, PL-35310 Rzeszow, Poland

[8] Lviv Natl Univ, 1 Univ St, UA-79602 Lvov, Ukraine

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 458卷 / 01期

关键词：

Inverse scattering problem; Schrodinger operator; Piecewise continuous impedance;

D O I：

10.1016/j.jmaa.2017.07.068

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the scattering problem for Schrodinger operators in impedance form, with step-like impedance functions. In this paper, the case where the jumps are located at the vertices of periodic lattice is considered. The set of reflection coefficients is completely described and the scattering map is shown to be homeomorphic. Also, an algorithm reconstructing the impedance function from the reflection coefficient is developed. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：71 / 92

页数：22

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