Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
type: Item
instance of: scholarly article
title: Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
zbMATH Open document ID: 1034.42040
DOI: 10.1023/A:1013959231555
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Bernstein polynomials are \[ B_L(x)=\sum_{\ell=0}^{L-1}{4L\choose \ell} x^{\ell}(1-x)^{4L-1}+ \sum_{\ell=L}^{3L-1}\left({3\over 2}-{\ell\over 2L}\right){4L\choose \ell} x^{\ell}(1-x)^{4L-1}, \quad L=1,2,\dots\,. \] The paper studies the distribution of the zeros of these polynomials when \(L\) is large. The zeros play a role in the construction of modified compactly supported wavelets. It is proved that the limiting curve for the zeros is the boundary of the domain of convergence of the Bernstein polynomials in the complex plane.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 33E20
zbMATH DE Number: 1928164
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: Daubechies wavelets
zbMATH Keywords: Riesz lemma
zbMATH Keywords: scaling function
zbMATH Keywords: incomplete beta function
author: I. Ya. Novikov
reviewed by: Nico M. Temme
MaRDI profile type: Publication
full work available at URL: a:1013959231555
OpenAlex ID: W4238437549
description: scientific article; zbMATH DE number 1928164