Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions

被引：71

作者：

Allahverdiev, Bilender P. ^{[1
]}

Bairamov, Elgiz ^{[2
]}

Ugurlu, Ekin ^{[2
]}

机构：

[1] Suleyman Demirel Univ, Dept Math, TR-32260 Isparta, Turkey

[2] Ankara Univ, Dept Math, TR-06100 Ankara, Turkey

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 401卷 / 01期

关键词：

Dissipative operators; Transmission condition; Eigenvalue problem; DIRECT SUM SPACES; EIGENVALUE PARAMETER; SPECTRAL PARAMETER; OPERATORS; THEOREM;

D O I：

10.1016/j.jmaa.2012.12.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the nonselfadjoint (dissipative) boundary value transmission problems in Weyl's limit-circle case. At first using the method of operator-theoretic formulation we pass to a new operator. After showing that this new operator is a maximal dissipative operator, we construct a selfadjoint dilation of the maximal dissipative operator. Using the equivalence of the Lax-Phillips scattering function and the Sz.-Nagy-Foia characteristic function, we show that all eigenfunctions and associated functions are complete in the space L-w(2)(Omega). (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：388 / 396

页数：9

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