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...
| Main Authors: | , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
2024
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/15246 |
| Summary: | 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. |
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