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Abstract
Recently it has been shown, that if a weight has the doubling property on its support [− 1,1], then the zeros of the associated orthogonal polynomials are uniformly spaced: if θm,j and θm,j+1 are the places in [0,π], for which cosθm,j and cosθm,j+1 is the j-th and the j+1-th zero of the m-th orthogonal polynomial, then θm,j − θm,j+1 ∼ 1/m. In this paper it is shown, that this result is also true in a local sense: if a weight has the doubling property in an interval of its support, then uniform spacing of the zeros is true inside that interval. The result contains as special cases some theorems of Last and Simon on local zero spacing of orthogonal polynomials.
Keywords: Doubling property; spacing of zeros; fast decreasing polynomials; Christoffel-function; Remez-inequality
Published Online: 2013-04-02
Published in Print: 2013-03
© by Oldenbourg Wissenschaftsverlag, München, Germany
