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

Máté, Attila ; Nevai, Paul

Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 106-122

Résumé

The main result of this paper concerns the eigenvalues of an operator in the Hilbert space l2 that 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

Détail

DOI : 10.4153/CJM-1989-005-5

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