The finite section method for dissipative operators

Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 and Naboko, Sergey 2014. The finite section method for dissipative operators. Mathematika 60 (2) , pp. 415-443. 10.1112/S0025579314000126

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Abstract

We show that for self-adjoint Jacobi matrices and Schrödinger operators, perturbed by dissipative potentials in ℓ 1 (N) and L 1 (0,∞) 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0025-5793 (accessed 05/06/2014)
Publisher:	London Mathematical Society/UCL Department of Mathematics
ISSN:	0025-5793
Funders:	Leverhulme Trust; Russian Foundation for Basic Research; Ukr.f.a. (Ukraine)
Date of First Compliant Deposit:	30 March 2016
Last Modified:	28 Nov 2024 07:00
URI:	https://orca.cardiff.ac.uk/id/eprint/59700

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