- Series
- Analysis Seminar
- Time
- Wednesday, September 23, 2009 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- Maxym Yattselev – Vanderbilt University
- Organizer
- Brett Wick
We consider multipoint Padé approximation to Cauchy transforms of
complex measures. First, we recap that if the support of a measure is
an analytic Jordan arc and if the measure itself is absolutely
continuous with respect to the equilibrium distribution of that arc
with Dini-continuous non-vanishing density, then the diagonal
multipoint Padé approximants associated with appropriate interpolation
schemes converge locally uniformly to the approximated Cauchy
transform in the complement of the arc. Second, we show that this
convergence holds also for measures whose Radon–Nikodym derivative is
a Jacobi weight modified by a Hölder continuous function. The
asymptotics behavior of Padé approximants is deduced from the analysis
of underlying non–Hermitian orthogonal polynomials, for which the
Riemann–Hilbert–∂ method is used.