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Erschienen in:
An Introduction to Orthogonal Polynomials Kapitel lesen Erstes Kapitel lesen

2020 | OriginalPaper | Buchkapitel

From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals

verfasst von : Juan C. García-Ardila, Francisco Marcellán, Misael E. Marriaga

Erschienen in: Orthogonal Polynomials

Verlag: Springer International Publishing

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Abstract

In this contribution, we present an overview of standard orthogonal polynomials by using an algebraic approach. Discrete Darboux transformations of Jacobi matrices are studied. Next, we emphasize the role of semiclassical orthogonal polynomials as a basic background to analyze sequences of polynomials orthogonal with respect to a Sobolev inner product. Some illustrative examples are discussed. Finally, we summarize some results in multivariate Sobolev orthogonal polynomials.

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Vorheriges Kapitel Some Characterization Problems Related to Sheffer Polynomial Sets
Nächstes Kapitel Two Variable Orthogonal Polynomials and Fejér-Riesz Factorization
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Metadaten
Titel
From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals
verfasst von
Juan C. García-Ardila
Francisco Marcellán
Misael E. Marriaga
Copyright-Jahr
2020
Buch
Orthogonal Polynomials

Print ISBN: 978-3-030-36743-5

Electronic ISBN: 978-3-030-36744-2

Copyright-Jahr: 2020

DOI
https://doi.org/10.1007/978-3-030-36744-2_13