Asymptotic distribution of zeros of polynomials satisfying difference equations
نویسندگان
چکیده
منابع مشابه
Orthogonal matrix polynomials satisfying second order difference equations
We develop a method that allows us to construct families of orthogonal matrix polynomials of size N ×N satisfying second order difference equations with polynomial coefficients. The existence (and properties) of these orthogonal families strongly depends on the non commutativity of the matrix product, the existence of singular matrices and the matrix size N .
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We consider ensembles of random polynomials of the form p(z) = ∑N j=1 ajPj where {aj} are independent complex normal random variables and where {Pj} are the orthonormal polynomials on the boundary of a bounded simply connected analytic plane domain Ω ⊂ C relative to an analytic weight ρ(z)|dz| . In the simplest case where Ω is the unit disk and ρ = 1, so that Pj(z) = z j , it is known that the ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(02)00564-2