Abstract
In this contribution, we study the sequences of orthogonal polynomials with respect to the Sobolev inner product
where μ is a nontrivial probability measure supported on the unit circle, α ∈ ℂ, \(\lambda \in {\mathbb{R}}_+\backslash\{0\}\), and j ∈ ℕ. In particular, we analyze the behavior of their zeros when n and λ tend to infinity, respectively. We also provide some numerical examples to illustrate the behavior of these zeros with respect to α.
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Dedicated to Professor Claude Brezinski and Professor Sebastiano Seatzu on the occasion of their 70th birthday.
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Castillo, K., Garza, L.E. & Marcellán, F. Zeros of Sobolev orthogonal polynomials on the unit circle. Numer Algor 60, 669–681 (2012). https://doi.org/10.1007/s11075-012-9594-6
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DOI: https://doi.org/10.1007/s11075-012-9594-6
Keywords
- Probability measures on the unit circle
- Orthogonal polynomials
- Sobolev inner products
- Hessenberg matrices
- Zeros