Asymptotics of the Roots of Bernstein Polynomials Used in the Construction of Modified Daubechies Wavelets

This paper is devoted to the study of the asymptotics of roots of a sequence of Bernstein polynomials approximating a piecewise linear function. This sequence arises in the construction of modified compactly supported wavelets that, in contrast to classical Daubechies wavelets, preserve localization with the growth of smoothness. It is proved that the limiting curve for roots is the boundary of the domain of convergence of the Bernstein polynomials on the complex plane.