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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 020, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.020 (Mi sigma1102) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations

Clotilde Martínez, Miguel A. Piñar

Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain
Full-text PDF (350 kB) Citations (7)
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DOI: https://doi.org/10.3842/SIGMA.2016.020
URL: https://www.emis.de/journals/SIGMA/2016/020/
Abstract: The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of spherical harmonics, algebraic and differential properties will be deduced.
Keywords: multivariate orthogonal polynomials; unit ball; partial differential equations.
Funding agency Grant number
Ministerio de Ciencia e Innovación de España MTM2011-28952-C02-02
European Regional Development Fund MTM2011-28952-C02-02
MTM2014-53171-P
Ministerio de Economía y Competitividad de España MTM2014-53171-P
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía P11-FQM-7276
This work has been partially supported by DGICYT, Ministerio de Economía y Competitividad (MINECO) of Spain and the European Regional Development Fund (ERDF) through grants MTM2011–28952–C02–02, MTM2014–53171–P, Reseach Project P11-FQM-7276 and Research Group FQM-384 from Junta de Andalucía.
Received: November 24, 2015; in final form February 18, 2016; Published online February 23, 2016
Bibliographic databases:
Document Type: Article
MSC: 33C50; 42C10
Language: English
Citation: Clotilde Martínez, Miguel A. Piñar, “Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations”, SIGMA, 12 (2016), 020, 11 pp.
Citation in format AMSBIB
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\paper Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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