Methods and Applications of Analysis

Companion Linear Functionals and Sobolev Inner Products: A Case Study

Antonia M. Delgado and Francisco Marcellan

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.

Article information

Source
Methods Appl. Anal., Volume 11, Number 2 (2004), 237-266.

Dates
First available in Project Euclid: 17 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.maa/1119019656

Mathematical Reviews number (MathSciNet)
MR2143522

Zentralblatt MATH identifier
1087.42020

Citation

Delgado, Antonia M.; Marcellan, Francisco. Companion Linear Functionals and Sobolev Inner Products: A Case Study. Methods Appl. Anal. 11 (2004), no. 2, 237--266. https://projecteuclid.org/euclid.maa/1119019656


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