POMATAC. PGC2018-094932-B-I00
MULTIVARIATE ORTHOGONAL POLYNOMIALS: THEORETICAL ASPECTS AND SCIENTIFIC APPLICATIONS
Research Project of the National Plan of I+D+i
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Funded by the Ministry of Sciences, Innovation and Universities (MICINN) of Spain and the European Regional
Development Fund (ERDF).
Call of 2018: Projects I+D for Generation of Knowledge, of the National Program for Development of Scientific Research and Technical Excellence of the I+D+i system.
Duration
- From 01/01/2019 until 12/31/2022.
Abstract
The general objective of the project is the improvement on the knowledge of the theory of Multivariate Orthogonal Polynomials, which are per se an interesting subject of research and, simultaneously show relevance in their scientific and technological applications.Multivariate orthogonal polynomials are not only a simple generalization of the polynomials in a single variable but they are indeed very complex mathematical objects with singular properties.
This Research Project can be seen as a extended continuation of the Research Projects: MTM2014-53171-P, MTM2011-28952-C02-02, MTM2008-06689-C02-02).
IPs
- Miguel A. Piñar, Universidad de Granada (Spain).
- Teresa E. Pérez, Universidad de Granada (Spain).
Research Team
- Antonia M. Delgado, Universidad de Granada (Spain).
- Lidia Fernández, Universidad de Granada (Spain).
Research Collaborators
- Carlos Beltrán, Universidad de Cantabria (Spain).
- Amílcar Branquinho, Universidade de Coimbra (Portugal).
- Cleconice F. Bracciali, Universidade Estadual Paulista (Brazil).
- Roberto Costas Santos, Universidad de Alcalá (Spain).
- Herbert Dueñas, Universidad Nacional de Colombia.
- Manuel Domínguez de la Iglesia, Universidad Autónoma de México.
- Ana Foulquié, Universidade de Aveiro (Portugal).
- Fátima Lizarte, Universidad de Cantabria (Spain).
- Francisco Marcellán, Universidad Carlos III de Madrid (Spain).
- Misael E. Marriaga, Universidad Rey Juan Carlos (Madrid, Spain).
- Joaquín Sánchez Lara, Universidad de Granada (Spain).
- Yuan Xu, University of Oregon (USA).
Publications
Preprints
- C. F. Bracciali, T. E. Pérez, Mixed orthogonality on the unit ball.
- M. Marriaga, T. E. Pérez, M. A. Piñar, Bivariate Koornwinder-Sobolev orthogonal polynomials.
- M. A. Piñar, Jackson's estimates on the weighted unit ball.
- M. A. Piñar, Christoffel functions on revolution solids and surfaces.
To appear
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L. Fernández, M. D. de la Iglesia,
Quasi-birth-and-death processes and multivariate orthogonal polynomials.
J. Math. Anal. Appl.
On line -
F. Lizarte, T. E. Pérez, M. A. Piñar,
The radial part of a class of Sobolev polynomials on the unit ball.
Numerical Algorithms
On line -
O. Salazar-Morales, H. A. Dueñas, M. A. Piñar
Sobolev orthogonal polynomials of several variables on product domains.
Medit. J. Math.
Year 2020
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A. M. Delgado, P. Iliev, L. Fernández,
Darboux transformation from the Appell-Lauricella operator.
J. Math. Anal. Appl. 482 (2020), 123546, 21 pp.
MR4015280 - F. Marcellán, M. E. Marriaga, T. E. Pérez, M. A. Piñar,
Geronimus transformations of bivariate linear functionals.
J. Math. Anal. Appl. 484 (2020), 123736, 30 pp.
MR4040130
Year 2019
- F. Marcellán, M. E. Marriaga, T. E. Pérez, M. A. Piñar,
Coherent pairs of bivariate orthogonal polynomilas
J. Approx. Theory 245 (2019), 40-63.
MR3945603 - C. Martínez, M. A. Piñar,
Asymptotic behaviour of the Christoffel functions on the
unit ball in the presence of a mass on the sphere.
Medit. J. Math.
16 (2019), no. 1, Art. 22, 18 pp.
MR3897518