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THE FINITE SECTION METHOD FOR DISSIPATIVE OPERATORS

Published online by Cambridge University Press:  14 May 2014

Marco Marletta
Affiliation:
Wales Institute of Mathematical and Computational Sciences, School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG,U.K. email [email protected]
Sergey Naboko
Affiliation:
School of Mathematics, Statistics and Actuarial Science, The University of Kent, Canterbury, Kent CT2 7NZ,U.K. email [email protected]
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Abstract

We show that for self-adjoint Jacobi matrices and Schrödinger operators, perturbed by dissipative potentials in $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\ell ^1({\mathbb{N}})$ and $L^1(0,\infty )$ respectively, the finite section method does not omit any points of the spectrum. In the Schrödinger case two different approaches are presented. Many aspects of the proofs can be expected to carry over to higher dimensions, particularly for absolutely continuous spectrum.

Type
Research Article
Copyright
Copyright © University College London 2014 

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