Dissipative eigenvalue problems for a singular Dirac system

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Allahverdiev B.

APPLIED MATHEMATICS AND COMPUTATION, vol.152, no.1, pp.127-139, 2004 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 152 Issue: 1
• Publication Date: 2004
• Doi Number: 10.1016/s0096-3003(03)00550-2
• Journal Name: APPLIED MATHEMATICS AND COMPUTATION
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.127-139
• Süleyman Demirel University Affiliated: Yes

Abstract

Dissipative singular Dirac operators are studied in the space L-A(2) ([a,b) ; C-2) (-infinity < a < b less than or equal to infinity), that the extensions of a minimal symmetric operator in Weyl's limit-point case. We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We construct a functional model of the dissipative operator and specify its characteristic function in terms of the Titchmarsh-Weyl function of selfadjoint operator. We prove theorems on completeness of the system of eigenvectors and associated vectors of the dissipative Dirac operators. (C) 2003 Elsevier Inc. All rights reserved.