Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System

被引：10
作者：
Fritzsche, B. [1 ]
Kirstein, B. [1 ]
Sakhnovich, A. L. [2 ]
机构：
[1] Univ Leipzig, Math Inst, Fak Math & Informat, D-04103 Leipzig, Germany
[2] Univ Vienna, Fak Math, A-1090 Vienna, Austria
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2010年 / 66卷 / 02期
基金：
奥地利科学基金会;
关键词：
Skew-self-adjoint Dirac system; Weyl function; inverse problem; semiseparable operator; operator identity; explicit solution; BLOCK TOEPLITZ MATRICES; EXTENSION PROBLEM; CANONICAL SYSTEMS; DIFFERENTIAL-EQUATIONS; SCATTERING PROBLEMS; SPECTRAL PROBLEM; DISCRETE; FORMULAS;
D O I：
10.1007/s00020-010-1739-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in terms of the Weyl function and a procedure to solve the inverse problem is given. The case of the generalized Weyl functions of the form phi(lambda) exp{-2i lambda D}, where phi is a strictly proper rational matrix function and D = D* >= 0 is a diagonal matrix, is treated in greater detail. Explicit formulas for the inversion of the corresponding semiseparable integral operators and recovery of the Dirac-type system are obtained for this case.
引用
收藏
页码：231 / 251
页数：21
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