How poles of orthogonal rational functions affect their Christoffel functions

We show that even a relatively small number of poles of a sequence of orthogonal rational functions approaching the interval of orthogonality, can prevent their Christoffel functions from having the expected asymptotics. We also establish a sufficient condition on the rate for such asymptotics, provided the rate of approach of the poles is sufficiently slow. This provides a supplement to recent results of the authors where poles were assumed to stay away from the interval of orthogonality. Orthogonal Rational Functions, Christoffel functions AMS Classification: 42C99 The work of the first author is partially supported by the Belgian Network DYSCO (Dynamical Systems, Control and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with the author. The first author is a Postdoctoral Fellow of the Research Foundation Flanders (FWO). Research of second author supported by NSF grant DMS1001182 and US-Israel BSF grant 2008399