SPECTRAL PROPERTIES OF THE SECOND ORDER DIFFERENCE EQUATION WITH SELFADJOINT OPERATOR COEFFICIENTS


Creative Commons License

MUTLU G.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.69, sa.1, ss.88-96, 2020 (ESCI İndekslerine Giren Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Konu: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.31801/cfsuasmas.562175
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.88-96

Özet

In this paper, we consider the second order difference equation defined on the whole axis with selfadjoint operator coefficients. The main objective of this study is to obtain the continuous and discrete spectrum of the discrete operator which is generated by this difference equation. To achieve this, we first obtain the Jost solutions of this equation explicitly and then examine the analytical and asymptotic properties of these solutions. With the help of these properties, we find the continuous and discrete spectrum of this operator. Finally we obtain a sufficient condition which ensures that this operator has a finite number of eigenvalues.