On Sobolev orthogonal polynomials on a triangle
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- by Misael E. Marriaga
- Proc. Amer. Math. Soc. 151 (2023), 679-691
- DOI: https://doi.org/10.1090/proc/16142
- Published electronically: July 22, 2022
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Abstract:
We use the invariance of the triangle $\mathbf {T}^2=\{(x,y)\in \mathbb {R}^2:\, 0\leqslant x,y,\, 1-x-y\}$ under the permutations of $\{x,y,1-x-y\}$ to construct and study two-variable orthogonal polynomial systems with respect to several distinct Sobolev inner products defined on $\mathbf {T}^2$. These orthogonal polynomials can be constructed from two sequences of univariate orthogonal polynomials. In particular, one of the two univariate sequences of polynomials is orthogonal with respect to a Sobolev inner product and the other is a sequence of classical Jacobi polynomials.References
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Bibliographic Information
- Misael E. Marriaga
- Affiliation: Departamento de Matemática Aplicada, Ciencia e Ingeniería de Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, Spain
- MR Author ID: 1201473
- ORCID: 0000-0002-7106-8593
- Email: misael.marriaga@urjc.es
- Received by editor(s): January 10, 2022
- Received by editor(s) in revised form: April 16, 2022, and April 27, 2022
- Published electronically: July 22, 2022
- Additional Notes: The author was supported by Ministerio de Ciencia, Innovación y Universidades (MICINN) grant PGC2018-096504-B-C33 and by the Comunidad de Madrid multiannual agreement with the Universidad Rey Juan Carlos under the grant Proyectos I+D para Jóvenes Doctores, Ref. M2731, project NETA-MM.
- Communicated by: Yuan Xu
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 679-691
- MSC (2020): Primary 33C50, 33D50; Secondary 33D45, 33C45
- DOI: https://doi.org/10.1090/proc/16142
- MathSciNet review: 4520018