3 research outputs found
Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set
For a system of two measures supported on a starlike set in the complex
plane, we study asymptotic properties of associated multiple orthogonal
polynomials and their recurrence coefficients. These measures are
assumed to form a Nikishin-type system, and the polynomials satisfy a
three-term recurrence relation of order three with positive coefficients. Under
certain assumptions on the orthogonality measures, we prove that the sequence
of ratios has four different periodic limits, and we
describe these limits in terms of a conformal representation of a compact
Riemann surface. Several relations are found involving these limiting functions
and the limiting values of the recurrence coefficients. We also study the th
root asymptotic behavior and zero asymptotic distribution of .Comment: 31 page