Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions

PAŞAOĞLU B., BAYRAM E., Ugurlu E.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.401, sa.1, ss.388-396, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 401 Sayı: 1
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.jmaa.2012.12.020
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.388-396
  • Anahtar Kelimeler: Dissipative operators, Transmission condition, Eigenvalue problem, DIRECT SUM SPACES, EIGENVALUE PARAMETER, SPECTRAL PARAMETER, OPERATORS, THEOREM
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we investigate the nonselfadjoint (dissipative) boundary value transmission problems in Weyl's limit-circle case. At first using the method of operator-theoretic formulation we pass to a new operator. After showing that this new operator is a maximal dissipative operator, we construct a selfadjoint dilation of the maximal dissipative operator. Using the equivalence of the Lax-Phillips scattering function and the Sz.-Nagy-Foia characteristic function, we show that all eigenfunctions and associated functions are complete in the space L-w(2)(Omega). (C) 2012 Elsevier Inc. All rights reserved.