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June 2004 Companion Linear Functionals and Sobolev Inner Products: A Case Study
Antonia M. Delgado, Francisco Marcellan
Methods Appl. Anal. 11(2): 237-266 (June 2004).

Abstract

The present paper deals with the solution of an inverse problem in the theory of orthogonal polynomials. It was motivated by a characterization result concerning sequences of polynomials orthogonal with respect to a Sobolev inner product when they can be recursively generated in terms of orthogonal polynomial sequences associated with the measure involved in the standard component. More precisely, we obtain the set of pairs of quasi-definite linear functionals such that their corresponding sequences of monic orthogonal polynomials {Pn} and {Rn} are related by a differential expression.

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Antonia M. Delgado. Francisco Marcellan. "Companion Linear Functionals and Sobolev Inner Products: A Case Study." Methods Appl. Anal. 11 (2) 237 - 266, June 2004.

Information

Published: June 2004
First available in Project Euclid: 17 June 2005

zbMATH: 1087.42020
MathSciNet: MR2143522

Rights: Copyright © 2004 International Press of Boston

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Vol.11 • No. 2 • June 2004
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