Reel eksende verilmiş kompleks potansiyele sahip Klein-Gordon s-dalga denkleminin spektral özellikleri
Spectral properties of the Klein-Gordon s-wave equation with complex potential on the whole real axis
- Tez No: 83414
- Danışmanlar: PROF.DR. ÖNER ÇAKAR
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1999
- Dil: Türkçe
- Üniversite: Ankara Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 73
Özet
Q, R. üzerinde sürekli diferensiyellenebilen ve /oo (l + \x\)\Q'(x)\dx
Özet (Çeviri)
In this study, we denote the operator L generated in the space Li by the Klein-Gordon s-wave equation y" + {k- Q{x))2y = 0, x ? R = (-00, 00) by L, where Q is complex valued potential function, continuously dif- ferentiable on R. satisfying the conditions /oo (I + \x\)\Q' {x)\dx < 00. -00 In the First Chapter, some basic definitions and main theorems on spectral analysis have been given. Also some earlier results are mentioned. In the Second Chapter, the Jost solutions of the operator L are defined and its properties are examined. Moreover, the functions D+(k) and D-(k) which play an important role in the following chapters are given. The Third and the Fourth Chapters of this thesis contain the original parts of the study. In the Third Chapter, the structure of the eigenvalues and the spec tral singularities of the operator L are examined considering the be haviour of the potential Q at infinity using the uniqueness theorem of analytic functions. We also find the conditions on the potential func tion Q under which the operator L has a finite number of eigenvalues and spectral singularities with finite multiplicities. mIn the Fourth Chapter, the properties of the principal functions corresponding the eigenvalues and the spectral singularities are inves tigated. We prove that the principal functions corresponding to the eigenvalues and the spectral singularities of the operator L belong to L2(K.) and H-, respectively. 1999, 63 pages Key Words : Spectral analysis, Jost solution, eigenvalue, spectral sin gularities, principal function
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