Projection Methods for Discrete Schrodinger Operators |
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Authors: | Boulton Lyonell |
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Affiliation: | Departmento de Matemáticas, Universidad Simón Bolívar Apartado 89000, Caracas 1080-A, Venezuela. E-mail: lboulton{at}ma.usb.ve |
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Abstract: | Let H be the discrete Schrödinger operator acting on l2 Z+, where the potential v is real-valued and v(n) 0 as n . Let P be the orthogonal projection onto a closedlinear subspace l2 Z+). In a recent paper E. B. Davies definesthe second order spectrum Spec2(H, ) of H relative to as theset of z C such that the restriction to of the operator P(H- z)2P is not invertible within the space . The purpose of thisarticle is to investigate properties of Spec2(H, ) when islarge but finite dimensional. We explore in particular the connectionbetween this set and the spectrum of H. Our main result providessharp bounds in terms of the potential v for the asymptoticbehaviour of Spec2(H, ) as increases towards l2 Z+). 2000 MathematicsSubject Classification 47B36 (primary), 47B39, 81-08 (secondary). |
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Keywords: | second order spectrum projection methods numerical approximation of the spectrum Jacobi operators |
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