Bauman Moscow State Technical University, Russia
Date(s) : 20/01/2014 iCal
10 h 00 min - 11 h 00 min
It is planned to discuss the questions on existence and boundary behavior of univalent functions in model subspaces (i.e. subspaces of the Hardy space H2 that are invariant under the backward shift operator; all such subspaces have the form KΘ = H2 ⊖ ΘH2, where Θ is an inner function). These questions are closely related with problems of boundary regularity of Nevanlinna domains (one recalls that bounded simply connected domain Ω in ℂ is called a Nevanlinna domain if there exist two functions u,v H∞(Ω), v non-zero, such that the equality z = u(z)∕v(z) holds almost everywhere on ∂Ω in the sense of conformal mappings). Nevanlinna domains, in turn, have recently and naturally appeared in problems of uniform approximability of functions by polyanalytic polynomials (i.e. by polynomials of the form znp n(z) + +zp1(z) + p0(z), where pn,…,p0 — are polynomials in the complex variable z) on compact subsets of the complex plane.