Orthogonal polynomials on radial rays in the complex plane: properties of zeros, Christoffel's formula, related moment problems and symmetries

We study a general class of orthogonal polynomials which, in particular, includes the following known classes of orthogonal polynomials: orthogonal polynomials on the real line, orthogonal polynomials on radial rays (with respect to a scalar positive Borel measure), discrete Sobolev orthogonal polynomials with a Sobolev measure concentrated at the origin. For this general class of polynomials we establish some basic properties of zeros, Christoffel's formula. We study the corresponding moment problems and some symmetric properties.

[1] S.M. Zagorodnyuk, Orthogonal polynomials on rays: properties of zeros, related moment problems and symmetries.- Journal of Mathematical Physics, Analysis, Geometry, 4, No. 3 (2008), 395-419.
[2] A. Choque Rivero, S.M. Zagorodnyuk, Orthogonal polynomials on rays: Christoffel's formula.- Submitted to a journal.