SPECTRAL MATRIX FOR STURM-LIOUVILLE OPERATORS ON TWO-SIDED UNBOUNDED TIME SCALES

Huseynov A.

JOURNAL OF OPERATOR THEORY, cilt.70, ss.33-51, 2013 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 70 Konu: 1
  • Basım Tarihi: 2013
  • Doi Numarası: 10.7900/jot.2011apr03.1923
  • Dergi Adı: JOURNAL OF OPERATOR THEORY
  • Sayfa Sayısı: ss.33-51

Özet

We establish existence of a spectral matrix for Sturm-Liouville operators on two-sided unbounded time scales. A Parseval equality and an expansion in eigenfunctions formula are obtained in terms of the spectral matrix. Our results unify and extend the well-known results on existence of a spectral matrix for Sturm-Liouville operators on the whole real axis and their discrete analogs.