Spectral properties of generalized eigenparameter dependent discrete Sturm-Liouville type equation

  • Turhan Koprubasi
  • R.N. Mohapatra
Keywords: Discrete equations, eigenparameter, spectral analysis, eigenvalues, spectral singularities, principal functions.

Abstract

Let L denote the non-selfadjoint difference operator of second order with boundary condition generated in ℓ2 (ℕ) by

an-1yn-1 + bnyn + anyn+1 = λyn ; n ∈ ℕ;   (0.1)
pΣk=0 (y1γk + y0βk) λk = 0;                    (0.2)

where {an} n∈ℕ and {bnn∈ℕ are complex sequences, γi; βi ∈ ℂ; i = 0; 1; 2; ...; p and
λ is a eigenparameter. Discussing the spectral properties of L, we investigate the
Jost function, spectrum, the spectral singularities, and the properties of the principal
vectors corresponding to the spectral singularities of L, if

Σn=1  n(∣1 - an∣ + ∣bnl) < ∞

Mathematics Subject Classication (2010): 34L05, 34L40, 39A70, 47A10, 47A75.

Key words: Discrete equations, eigenparameter, spectral analysis, eigenvalues, spectral
singularities, principal functions.

Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606