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Proceedings of the American Mathematical Society

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Fourth order partial differential equations for Krall-type orthogonal polynomials on the triangle


Authors: Antonia M. Delgado, Lidia Fernández and Teresa E. Pérez
Journal: Proc. Amer. Math. Soc. 146 (2018), 3961-3974
MSC (2010): Primary 33C50, 42C05
DOI: https://doi.org/10.1090/proc/14052
Published electronically: May 24, 2018
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Abstract: We construct bivariate polynomials orthogonal with respect to a Krall-type inner product on the triangle defined by adding Krall terms over the border and the vertexes to the classical inner product. We prove that these Krall-type orthogonal polynomials satisfy fourth order partial differential equations with polynomial coefficients, as an extension of the classical theory introduced by H. L. Krall in the 1940s.


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Antonia M. Delgado
Affiliation: Departamento de Matemática Aplicada & Instituto de Matemáticas (IEMath - GR) Universidad de Granada. 18071. Granada, Spain
Email: amdelgado@ugr.es

Lidia Fernández
Affiliation: Departamento de Matemática Aplicada & Instituto de Matemáticas (IEMath - GR) Universidad de Granada. 18071. Granada, Spain
Email: lidiafr@ugr.es

Teresa E. Pérez
Affiliation: Departamento de Matemática Aplicada & Instituto de Matemáticas (IEMath - GR) Universidad de Granada. 18071. Granada, Spain
Email: tperez@ugr.es

DOI: https://doi.org/10.1090/proc/14052
Keywords: Orthogonal polynomials on the triangle, low dimensional Krall-type modification, fourth order partial differential equations
Received by editor(s): March 24, 2017
Received by editor(s) in revised form: September 19, 2017, December 5, 2017, and December 12, 2017
Published electronically: May 24, 2018
Additional Notes: This work has been partially supported by MINECO of Spain and the European Regional Development Fund (ERDF) through grant MTM2014-53171-P, and by Junta de Andalucía grant P11-FQM-7276 and research group FQM-384.
The third author is the corresponding author.
Communicated by: Yuan Xu
Article copyright: © Copyright 2018 American Mathematical Society