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Eigenvalues of Finite Band-Width Hilbert Space Operators and Their Application to Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

Attila Máté  and
Paul Nevai
Attila Máté
Affiliation:
Florida International University, Miami, Florida
Paul Nevai
Affiliation:
Florida International University, Miami, Florida
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The main result of this paper concerns the eigenvalues of an operator in the Hilbert space l2that is represented by a matrix having zeros everywhere except in a neighborhood of the main diagonal. Write (c)+ for the positive part of a real number c, i.e., put (c+ = cif c≧ 0 and (c)+=0 otherwise. Then this result can be formulated as follows. Theorem 1.1. Let k ≧ 1 be an integer, and consider the operator S on l2 such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 1 , 01 February 1989 , pp. 106 - 122
Copyright
Copyright © Canadian Mathematical Society 1989

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