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SPECTRAL BOUNDS USING HIGHER ORDER NUMERICAL RANGES

By E B Davies

Abstract

We describe how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what we call its higher order numerical ranges. We prove some of their basic properties and describe explain how to compute them. We finally use them to obtain new spectral insights into the non-selfadjoint Anderson model in one and two space dimensions

Topics: non-self-adjoint operator, spectrum, numerical range, Anderson model, ergodic Schrödinger operator, Airy operator, pseudospectrum
Year: 2004
OAI identifier: oai:CiteSeerX.psu:10.1.1.160.8183
Provided by: CiteSeerX
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