Expected number of real zeros for random Freud orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Expected Number of Real Zeros for Random Linear Combinations of Orthogonal Polynomials
We study the expected number of real zeros for random linear combinations of orthogonal polynomials. It is well known that Kac polynomials, spanned by monomials with i.i.d. Gaussian coefficients, have only (2/π + o(1)) logn expected real zeros in terms of the degree n. On the other hand, if the basis is given by Legendre (or more generally by Jacobi) polynomials, then random linear combinations...
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Let pnðxÞ be the orthonormal polynomials associated to a measure dm of compact support in R: If EesuppðdmÞ; we show there is a d40 so that for all n; either pn or pnþ1 has no zeros in ðE d;E þ dÞ: If E is an isolated point of suppðmÞ; we show there is a d so that for all n; either pn or pnþ1 has at most one zero in ðE d;E þ dÞ:We provide an example where the zeros of pn are dense in a gap of su...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.04.068