Asymptotic zero distribution of biorthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Asymptotic 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 کاملBiorthogonal polynomials and zero-mapping transformations
The authors have presented in [6] a technique to generate transformations T of the set Pn of nth degree polynomials to itself such that if p ∈ Pn has all its zeros in (c, d) then T {p} has all its zeros in (a, b), where (a, b) and (c, d) are given real intervals. The technique rests upon the derivation of an explicit form of biorthogonal polynomials whose Borel measure is strictly sign consiste...
متن کاملAsymptotic zero distribution of random polynomials spanned by general bases
Zeros of Kac polynomials spanned by monomials with i.i.d. random coefficients are asymptotically uniformly distributed near the unit circumference. We give estimates of the expected discrepancy between the zero counting measure and the normalized arclength on the unit circle. Similar results are established for polynomials with random coefficients spanned by different bases, e.g., by orthogonal...
متن کاملZero 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.01.001