Non-self-adjoint singular second-order dynamic operators on time scale
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.42, sa.1, ss.229-236, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 1
- Basım Tarihi: 2019
- Doi Numarası: 10.1002/mma.5338
- Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.229-236
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
In this study, maximal dissipative second-order dynamic operators on semi-infinite time scale are studied in the Hilbert space Lr2(T+), that the extensions of a minimal symmetric operator in limit-point case. We construct a self-adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax-Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl-Titchmarsh function of a self-adjoint second-order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.