Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.

DOI10.1023/A:1013959231555zbMath1034.42040OpenAlexW4238437549MaRDI QIDQ1810065

Igor Ya. Novikov

Publication date: 15 June 2003

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1013959231555

zbMATH Keywords

incomplete beta functionBernstein polynomialsscaling functionDaubechies waveletsRiesz lemma

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Other functions defined by series and integrals (33E20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (15)

Generalized Popoviciu expansions for Bernstein polynomials of a rational module ⋮ On the \(q\)-Bernstein polynomials of unbounded functions with \(q > 1\) ⋮ The functional-analytic properties of the limit \(q\)-Bernstein operator ⋮ Unnamed Item ⋮ The \(q\)-Bernstein polynomials of the Cauchy kernel with a pole on \([0,1\) in the case \(q>1\)] ⋮ The norm estimates of the \(q\)-Bernstein operators for varying \(q>1\) ⋮ Computer analysis of the attractors of zeros for classical Bernstein polynomials ⋮ A generalization of Jentzsch's theorem ⋮ On the \(q\)-Bernstein polynomials of piecewise linear functions in the case \(q>1\) ⋮ On the eigenvectors of the q -Bernstein operators ⋮ The norm estimates for the $q$-Bernstein operator in the case $q>1$ ⋮ On the analyticity of functions approximated by their \(q\)-Bernstein polynomials when \(q > 1\) ⋮ On the \(q\)-Bernstein polynomials of rational functions with real poles ⋮ The sharpness of convergence results for q-Bernstein polynomials in the case q > 1 ⋮ On the eigenstructure of the $(\alpha,q)$-Bernstein operator

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