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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 090, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.090 (Mi sigma1172) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Multivariate Orthogonal Polynomials and Modified Moment Functionals

Antonia M. Delgado, Lidia Fernández, Teresa E. Pérez, Miguel A. Piñar

IEMath – Math Institute and Department of Applied Mathematics, University of Granada, 18071, Granada, Spain
Full-text PDF (466 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2016.090
Abstract: Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to the moment functional a finite set of mass points, or by multiplying it times a polynomial of total degree $2$, respectively. Orthogonal polynomials associated with modified moment functionals will be studied, as well as the impact of the modification in useful properties of the orthogonal polynomials. Finally, some illustrative examples will be given.
Keywords: multivariate orthogonal polynomials; moment functionals; Christoffel modification; Uvarov modification; ball polynomials.
Funding agency Grant number
European Regional Development Fund MTM2014-53171-P
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía P11-FQM-7276
FQM-384
This work has been partially supported by MINECO of Spain and the European Regional Development Fund (ERDF) through grant MTM2014–53171–P, and Junta de Andalucía grant P11–FQM–7276 and research group FQM–384.
Received: January 28, 2016; in final form September 5, 2016; Published online September 10, 2016
Bibliographic databases:
Document Type: Article
MSC: 33C50; 42C10
Language: English
Citation: Antonia M. Delgado, Lidia Fernández, Teresa E. Pérez, Miguel A. Piñar, “Multivariate Orthogonal Polynomials and Modified Moment Functionals”, SIGMA, 12 (2016), 090, 25 pp.
Citation in format AMSBIB
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\paper Multivariate Orthogonal Polynomials and Modified Moment Functionals
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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