Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle

Authors:
E. B. Davies;B. Simon
Affiliations:
Department of Mathematics, King's College London, Strand, London, UK;Mathematics, California Institute of Technology, Pasadena, CA
Venue:
Journal of Approximation Theory
Year:
2006

Citing 2
Cited 1

I. Schur methods inoperator theory and signal processing

I. Schur methods inoperator theory and signal processing
The statistical distribution of the zeros of random paraorthogonal polynomials on the unit circle

Journal of Approximation Theory

Poisson brackets of orthogonal polynomials

Journal of Approximation Theory

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Abstract

We prove that for any n × n matrix, A, and z with |z| ≥ ||A||, we have that ||(z - A)-1|| ≤ cot(π/4n) dist(z, spec(A))-1. We apply this result to the study of random orthogonal polynomials on the unit circle.