SCATTERING AND SPECTRAL PROBLEMS OF THE DIRECT SUM STURM-LIOUVILLE OPERATORS
APPLIED AND COMPUTATIONAL MATHEMATICS, cilt.16, sa.3, ss.257-268, 2017 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 3
- Basım Tarihi: 2017
- Dergi Adı: APPLIED AND COMPUTATIONAL MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
- Sayfa Sayıları: ss.257-268
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
In this paper a space of boundary values is constructed for direct sum minimal symmetric Sturm-Liouville operators and description of all maximal dissipative, maximal accumulative, selfadjoint and other extensions of such a symmetric operator is given in terms of boundary conditions. We construct a selfadjoint dilation of dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on completeness of the system of eigenfunctions and associated functions of the dissipative operators.