منابع مشابه
Zero Distribution of Random Polynomials
We study global distribution of zeros for a wide range of ensembles of random polynomials. Two main directions are related to almost sure limits of the zero counting measures, and to quantitative results on the expected number of zeros in various sets. In the simplest case of Kac polynomials, given by the linear combinations of monomials with i.i.d. random coefficients, it is well known that th...
متن کاملAsymptotic zero distribution of biorthogonal polynomials
Let ψ : [0, 1] → R be a strictly increasing continuous function. Let Pn be a polynomial of degree n determined by the biorthogonality conditions ∫ 1 0 Pn (x)ψ (x) j dx = 0, j = 0, 1, . . . , n− 1. We study the distribution of zeros of Pn as n → ∞, and related potential theory.
متن کاملZero Distribution of Composite Polynomials and Polynomials Biorthogonal to Exponentials
We analyze polynomials Pn that are biorthogonal to exponentials {e−σn,j }j=1, in the sense that ∫ ∞ 0 Pn(x)e −σn,j x dx = 0, 1 ≤ j ≤ n. Here α >−1. We show that the zero distribution of Pn as n→∞ is closely related to that of the associated exponent polynomial Qn(y)= n ∏ j=1 (y + 1/σn,j )= n ∑ j=0 qn,j y j . More precisely, we show that the zero counting measures of {Pn(−4nx)}∞n=1 converge weak...
متن کاملZero Asymptotic Behaviour for Orthogonal Matrix Polynomials
Weak-star asymptotic results are obtained for the zeros of orthogonal matrix polynomials (i.e. the zeros of their determinants) on R from two di®erent assumptions: ̄rst from the convergence of matrix coe±cients occurring in the three-term recurrence for these polynomials and, second, from some conditions on the generating matrix measure. The matrix analogue of the Chebyshev polynomials of the ̄...
متن کاملZero Distribution of Sequences of Classical Orthogonal Polynomials
In this paper, we study the zero distribution of sequences of Jacobi, Laguerre, and Hermite polynomials. Our approach is based on identifying these orthogonal polynomials with certain Fekete polynomials defined below, and using monotonicity properties of the zeros of the polynomials. Let E ⊂ R be a closed set that consists of finitely many intervals. Let w : E→ [0,∞) be a weight function such t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.04.001