A dissipative singular Sturm-Liouville problem with a spectral parameter in the boundary condition


Allahverdiev B.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.316, ss.510-524, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 316 Konu: 2
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.jmaa.2005.04.071
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.510-524

Özet

In the Hilbert space L-w(2) (a, b), we consider nonselfadjoint singular Sturm-Liouville boundary value problem (with two singular end points a and b) in limit-circle cases at a and b, and with a spectral parameter in the boundary condition. The approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Sturm-Liouville equation. On the basis of the results obtained regarding the theory of the characteristic function, we prove theorems on completeness of the system of eigenvectors and associated vectors of the maximal dissipative operator and Sturm-Liouville boundary value problem. (c) 2005 Elsevier Inc. All rights reserved.