A spectral expansion for Schrödinger operator

BAŞCANBAZ TUNCA G.

Proyecciones, cilt.25, sa.1, ss.63-78, 2006 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 1
  • Basım Tarihi: 2006
  • Dergi Adı: Proyecciones
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.63-78
  • Anahtar Kelimeler: Spectral expansion, Spectrum, Weyl function
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper we consider the Schrödinger operator L generated in L2 (R+) by y″ + q(x)y = μy, x ∈ R+:= [0, ∞) subject to the boundary condition y′ (0) - hy (0) = 0, where,q is a complex valued function summable in [0, ∞ and h ≠ 0 is a complex constant, μ is a complex parameter. We have assumed that supx∈R+ {exp (ε√x) q(x) } < ∞, ε > 0, holds which is the minimal condition that the eigenvalues and the spectral singularities of the operator L are finite with finite multiplicities. Under this condition we have given the spectral expansion formula for the operator L using an integral representation for the Weyl function of L. Moreover we also have investigated the convergence of the spectral expansion. © 2006 Universidad Católica del Norte, Departamento de Matemáticas.