The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on June 17, 2014 at 14:00 in Room 478 of IMI.

A talk on:

„Maximally Convergent Sequences of Rational Functions: Growth Behavior and Zero Distribution”

will be delivered by prof. Ralitza Kovacheva.

Everybody is invited.

Abstract.
We investigate the growth and the distribution of zeros of rational uniform approximations with numerator degree ≤ n and denominator degree ≤ m_n for meromorphic functions f  on a compact set E of C where m_n = o(n) as n → ∞. We obtain a Jentzsch-Szegő type result, i.e., the zero distribution converges weakly to the equilibrium distribution of the maximal Green domain E _ρ(f)  of meromorphy of f  if f  has a singularity of multivalued character on the boundary of E _ρ(f). The paper extends results for polynomial approximation and rational approximation with fixed degree of the denominator. As applications, Padé approximation and real rational best approximants are considered...