Abstract
It is shown that for doubling weights, the zeros of the associated orthogonal polynomials are uniformly spaced in the sense that if cos θ m,k, θ m,k∈[0,π] are the zeros of the m-th orthogonal polynomial associated with w, then θ m,k−θ m,k+1∼1/m. It is also shown that for doubling weights, neighboring Cotes numbers are of the same order. Finally, it is proved that these two properties are actually equivalent to the doubling property of the weight function.
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Communicated by Serguei Denissov.
Research of the first author was supported by Italian Ministero dell’Università e della Ricerca, PRIN 2006 “Numerical methods for structured linear algebra and applications.”
Research of the second author was supported by NSF grant DMS 0700471.
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Mastroianni, G., Totik, V. Uniform Spacing of Zeros of Orthogonal Polynomials. Constr Approx 32, 181–192 (2010). https://doi.org/10.1007/s00365-009-9047-1
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DOI: https://doi.org/10.1007/s00365-009-9047-1