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arXiv · 1907.13226

Classical Sobolev orthogonal polynomials: eigenvalue problem

Juan F. Mañas-Mañas·Juan J. Moreno-Balcázar
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Abstract

We consider the discrete Sobolev inner product $$(f,g)_S=\int f(x)g(x)dμ+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad c\in\mathbb{R}, \quad M>0, $$ where $μ$ 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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Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar. 2019-07-30. Classical Sobolev orthogonal polynomials: eigenvalue problem. https://doi.org/10.1007/s00025-019-1069-9

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