On the half inverse spectral problem for an integro-differential operator

Buterin S. A., Sat M.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, cilt.25, sa.10, ss.1508-1518, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 10
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/17415977.2016.1267171
  • Dergi Adı: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1508-1518
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

We consider the Sturm-Liouville differential operator on a finite interval with Dirichlet boundary conditions perturbed with a convolution integral operator. The inverse problem is studied of recovering the convolution kernel from a half spectrum, provided that the kernel function on the first half of the interval as well as the Sturm-Liouville potential on the entire interval are known a priori. Besides the uniqueness of a solution of this half inverse problem, we also obtain necessary and sufficient conditions of its solvability. A constructive procedure for solving the inverse problem is also provided.