Equilibrium measure and limit zeros distribution of extremal weighted polynomials
نویسندگان
چکیده
منابع مشابه
Equilibrium Distribution of Zeros of Random Polynomials
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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For −1 < α ≤ 0 and 0 < p < ∞, the solutions of certain extremal problems are known to act as contractive zerodivisors in the weighted Bergman space Aα. We show that for 0 < α ≤ 1 and 0 < p < ∞, the analogous extremal functions do not have any extra zeros in the unit disk and, hence, have the potential to act as zero-divisors. As a corollary, we find that certain families of hypergeometric funct...
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Article history: Received 4 September 2014 Available online 16 March 2016
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1994
ISSN: 0893-9659
DOI: 10.1016/0893-9659(94)90015-9