Bernstein-Szego-Lebesgue Sobolev orthogonal polynomials on the unit circle

In this paper we consider the following continuous Sobolev inner product on the unit circle <f(z), g(z)> (s) = integral (2 pi)(0)f(e(i theta))g(e(i theta))d mu(theta) + 1/lambda integral (2 pi)(0) f'(e(i theta))g'(e(i theta))d theta /2 pi, z = e(i theta), where lambda > 0, d mu(theta) is a Bernstein-Szego measure and d theta /2 pi is the normalized Lebesgue measure on [0, 2 pi]. We study the corresponding sequence of orthogonal polynomials. Algebraic properties, asymptotic behavior and asymptotic distribution of zeros for such polynomials are obtained.