Eigenvalues of Finite Band-Width Hilbert Space Operators and Their Application to Orthogonal Polynomials
- 1 February 1989
- journal article
- research article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 41 (1) , 106-122
- https://doi.org/10.4153/cjm-1989-005-5
Abstract
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 thatThis publication has 3 references indexed in Scilit:
- Twisted difference operators and perturbed Chebyshev polynomialsDuke Mathematical Journal, 1988
- Orthogonal polynomials and measures with finitely many point massesJournal of Approximation Theory, 1982
- Linear Transformations in Hilbert Space and Their Applications to AnalysisPublished by American Mathematical Society (AMS) ,1932