Classical Sobolev orthogonal polynomials: eigenvalue problem
We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal polynomi...
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2024
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| Online Access: | http://hdl.handle.net/10835/15246 |
| _version_ | 1789406472334999552 |
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| author | Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José |
| author_facet | Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José |
| author_sort | Mañas Mañas, Juan Francisco |
| collection | DSpace |
| description | We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal polynomials with respect to this Sobolev inner product are eigenfunctions of a differential operator and obtaining the asymptotic behavior of the corresponding eigenvalues is the principal goal of this paper. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-15246 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2024 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-152462024-01-18T08:18:51Z Classical Sobolev orthogonal polynomials: eigenvalue problem Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José Sobolev orthogonal polynomials Differential operator Eigenvalues Asymptotics We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal polynomials with respect to this Sobolev inner product are eigenfunctions of a differential operator and obtaining the asymptotic behavior of the corresponding eigenvalues is the principal goal of this paper. 2024-01-18T08:18:50Z 2024-01-18T08:18:50Z 2019-07 info:eu-repo/semantics/article Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar. Classical Sobolev orthogonal polynomials: eigenvalue problem Results Math. 74 (2019), Art. 144. 1422-6383 http://hdl.handle.net/10835/15246 en Grant MTM2017-89941-P and grant SOMM17/6105/UGR. Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar. Classical Sobolev orthogonal polynomials: eigenvalue problem Results Math. 74 (2019), Art. 144. |
| spellingShingle | Sobolev orthogonal polynomials Differential operator Eigenvalues Asymptotics Mañas Mañas, Juan Francisco Moreno Balcázar, Juan José Classical Sobolev orthogonal polynomials: eigenvalue problem |
| title | Classical Sobolev orthogonal polynomials: eigenvalue problem |
| title_full | Classical Sobolev orthogonal polynomials: eigenvalue problem |
| title_fullStr | Classical Sobolev orthogonal polynomials: eigenvalue problem |
| title_full_unstemmed | Classical Sobolev orthogonal polynomials: eigenvalue problem |
| title_short | Classical Sobolev orthogonal polynomials: eigenvalue problem |
| title_sort | classical sobolev orthogonal polynomials: eigenvalue problem |
| topic | Sobolev orthogonal polynomials Differential operator Eigenvalues Asymptotics |
| url | http://hdl.handle.net/10835/15246 |
| work_keys_str_mv | AT manasmanasjuanfrancisco classicalsobolevorthogonalpolynomialseigenvalueproblem AT morenobalcazarjuanjose classicalsobolevorthogonalpolynomialseigenvalueproblem |