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When Does a Discrete Differential Perturbation of a Sequence of Orthonormal Polynomials Belong tol2?

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
136
Issue
1
Identifiers
DOI: 10.1006/jfan.1996.0024

Abstract

Abstract Let μ be a positive determinate measure with moments of every order and infinite support and let ( p n ) n be the corresponding sequence of orthonormal polynomials. Let ( z 1, k 1), …, ( z N , k N ) be given, where the z's are different complex numbers and the k's are nonnegative integers. We characterize the operators of the form T=∑ N l=1 ∑ k l j=0 a l, j δ ( j) z l , for which the sequence ( T( p n )) n belongs to ℓ 2.

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