Quadratic Pencil of Difference Equations: Jost Solutions, Spectrum, and Principal Vectors
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- 30 November 2010
- journal article
- Published by National Inquiry Services Center (NISC) in Quaestiones Mathematicae
- Vol. 33 (3) , 305-323
Abstract
In this paper, a quadratic pencil of Schrodinger type difference operator Lλ is taken under investigation to provide a general perspective for the spectral analysis of non-selfadjoint difference equations of second order. Introducing Jost-type solutions, structure and quantitative properties of the spectrum of Lλ are investigated. Therefore, a discrete analog of the theory in [6] and [7] is developed. In addition, several analogies are established between difference and q-difference cases. Finally, the principal vectors of Lλ are introduced to lay a groundwork for the spectral expansion.Keywords
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This publication has 12 references indexed in Scilit:
- Spectral analysis of -difference equations with spectral singularitiesMathematical and Computer Modelling, 2006
- Spectral Properties of the Nonhomogeneous Klein-Gordon s -Wave EquationsRocky Mountain Journal of Mathematics, 2004
- Spectral Properties, Including Spectral Singularities, of a Quadratic Pencil of Schrödinger Operators on the Whole Real AxisQuaestiones Mathematicae, 2003
- Difference equations of second order with spectral singularitiesJournal of Mathematical Analysis and Applications, 2003
- Spectral Properties of Non-selfadjoint Difference OperatorsJournal of Mathematical Analysis and Applications, 2001
- Spectrum and Spectral Singularities of a Quadratic Pencil of a Schrödinger Operator with a General Boundary ConditionJournal of Differential Equations, 1999
- Representation theory approach to the polynomial solutions of q-difference equations: Uq(sl(3)) and beyondJournal of Mathematical Physics, 1994
- Boundary-value uniqueness theorems for analytic functionsMathematical Notes, 1979
- The inverses-wave scattering problem for a class of potentials depending on energyCommunications in Mathematical Physics, 1972
- On the Inverse Problem for the Klein-Gordon s-Wave EquationJournal of Mathematical Physics, 1970