Quadratic eigenparameter-dependent quantum difference equations

AYGAR KÜÇÜKEVCİLİOĞLU Y.

TURKISH JOURNAL OF MATHEMATICS, cilt.40, sa.2, ss.445-452, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3906/mat-1507-2
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.445-452
  • Anahtar Kelimeler: q-difference equation, Jost solution, spectral analysis, eigenvalue, spectral singularity, SPECTRAL PROPERTIES
  • Ankara Üniversitesi Adresli: Evet

Özet

The main aim of this paper is to construct quantum extension of the discrete Sturm Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. We present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.