scholarly journals Local asymptotic distribution of zeros of orthogonal polynomials

1994 ◽  
Vol 341 (2) ◽  
pp. 881-894 ◽  
Author(s):  
Vilmos Totik ◽  
Joseph L. Ullman
Keyword(s):  
Orthogonal Polynomials ◽  
Asymptotic Distribution ◽  
Distribution Of Zeros ◽  
Zeros Of Orthogonal Polynomials ◽  
Asymptotic Distribution Of Zeros

scholarly journals CONVERGENCE OF FUBINI–STUDY CURRENTS FOR ORBIFOLD LINE BUNDLES

2013 ◽  
Vol 24 (07) ◽  
pp. 1350051 ◽  
Author(s):  
DAN COMAN ◽  
GEORGE MARINESCU
Keyword(s):  
Line Bundle ◽  
Asymptotic Distribution ◽  
Line Bundles ◽  
Singular Line ◽  
Distribution Of Zeros ◽  
Bergman Kernels ◽  
Holomorphic Sections ◽  
Asymptotic Distribution Of Zeros

We discuss positive closed currents and Fubini–Study currents on orbifolds, as well as Bergman kernels of singular Hermitian orbifold line bundles. We prove that the Fubini–Study currents associated to high powers of a semipositive singular line bundle converge weakly to the curvature current on the set where the curvature is strictly positive, generalizing a well-known theorem of Tian. We include applications to the asymptotic distribution of zeros of random holomorphic sections.

scholarly journals On the Distribution of Zeros and Poles of Rational Approximants on Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
V. V. Andrievskii ◽  
H.-P. Blatt ◽  
R. K. Kovacheva
Keyword(s):  
Asymptotic Distribution ◽  
Polynomial Approximation ◽  
Additional Assumption ◽  
Equilibrium Measure ◽  
Distribution Of Zeros ◽  
Rational Approximants ◽  
Bounded Degree ◽  
Asymptotic Distribution Of Zeros ◽  
Best Rational Approximants ◽  
Zeros And Poles

The distribution of zeros and poles of best rational approximants is well understood for the functions , . If is not holomorphic on , the distribution of the zeros of best rational approximants is governed by the equilibrium measure of under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, -values, and poles of best real rational approximants of degree at most to a function that is real-valued, but not holomorphic on . Generalizations to the lower half of the Walsh table are indicated.

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