prof. Pavel Stovicek (Praha)

Orthogonal polynomials, Jacobi matrices and the moment problem. A survey of the general theory and selected new results

A brief survey of the theory of orthogonal polynomials is given including the fundamental recurrence relation and Favard's theorem, the Hamburger moment problem and its solution in terms of the Nevanlinna parametrization of probability measures in the indeterminate case, a relationship to the self-adjoint extensions of the associated Jacobi matrix and properties of the zeros of an orthogonal polynomial sequence. Furthermore, selected new results concerning a generalization of the Lommel polynomials are presented; a complete description can be found in the recent publication: F. Stampach, P. Stovicek: Orthogonal polynomials associated with Coulomb wave functions, J. Math. Anal. Appl. (2014), in press, available online, http://dx.doi.org/10.1016/j.jmaa.2014.04.049 .