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Quadratic Pencil of Schrödinger Operators with Spectral Singularities: Discrete Spectrum and Principal Functions

✍ Scribed by Elgiz Bairamov; Öner Çakar; A.Okay Çelebi

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 245 KB
Volume: 216
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5689

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✦ Synopsis

In this article we investigated the spectrum of the quadratic pencil of Schro-Ž .

Ž . dinger operators L generated in L ‫ޒ‬ by the equation 2 q 2 w yyЉ q V x q 2U x y y s 0, x g ‫ޒ‬ s 0, ϱ 2 q Ž . about the spectrum of L have also been applied to radial Klein᎐Gordon and one-dimensional Schrodinger equations.

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## Abstract We show that when a potential __b~n~__ of a discrete Schrödinger operator, defined on __l__^2^(ℤ^+^), slowly oscillates satisfying the conditions __b~n~__ ∈ __l__^∞^ and ∂__b~n~__ = __b__~__n__ +1~ – __b~n~__ ∈ __l^p^__, __p__ < 2, then all solutions of the equation __Ju__ = __Eu__ are