On Sobolev orthogonal polynomials

• Published in: Expositiones mathematicae Vol. 33; no. 3; pp. 308 - 352
• Main Authors: Marcellán, Francisco, Xu, Yuan
• Format: Journal Article
• Language: English
• Published: Elsevier GmbH 01-01-2015
• Subjects: Approximation by polynomials; Orthogonal polynomials; Sobolev orthogonal polynomials; secondary; Approximation by polynomials; Sobolev orthogonal polynomials; Orthogonal polynomials; primary
• ISSN: 0723-0869; 1878-0792
• DOI: 10.1016/j.exmath.2014.10.002

Sobolev orthogonal polynomials have been studied extensively in the past quarter-century. The research in this field has sprawled into several directions and generates a plethora of publications. This paper contains a survey of the main developments up to now. The goal is to identify main ideas and developments in the field, which hopefully will lend a structure to the mountainous publications and help future research.