Joel Langer
Department of Mathematics
Case Western Reserve University
Interpolation by rational diffeomorphisms of the circle
The theory of interpolation by rational functions is a highly developed subject, which continues to receive attention---not only because of its intrinsic beauty and mathematical interest, but also because of a variety of applications, e.g., in signal processing, circuit theory, robust stabilization and stochastic control theory. In view of well-known stability criteria, it is not surprising that the modern literature (like the classical Nevanlinna-Pick theory) has dealt with functions whose poles are restricted at the outset to lie in a suitable subdomain. On the other hand, from the point of view of certain geometrical or dynamical considerations, one would like to have techniques for constructing rational circle diffeomorphisms---imposing a rather different analytical condition (while allowing a priori nearly arbitrary pole placement). This talk will present a simple interpolation result in the latter context, and briefly indicate the geometrical origins of the problem.