On oscillatory properties of the Bernstein-Szegő orthogonal polynomials (Q1849196)

The author investigates the mutual relationships of oscilations of the Bernstein-Szegő orthogonal polynomials (B-SOP) of different kinds in the boundaries. The boundaries are determined by the weight functions with indication of Chebyshev's alternances. The B-SOP generalize the classical Chebyshev polynomials by introducing an arbitrary positive polynomial advisor into the weight function, which significantly extend the theoretical and applied capabilities of this system.