5 papers
Critical structures of inner functions
Oleg Ivrii
A celebrated theorem of M. Heins says that up to post-composition with a Möbius transformation, a finite Blaschke product is uniquely determined by its critical points. K. Dyakonov…
Homogenization of random quasiconformal mappings and random Delauney triangulations
Oleg Ivrii, Vladimir Markovic
In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle pac…
Simultaneous zero-free approximation and universal optimal polynomial approximants
Catherine Bénéteau, Oleg Ivrii, Myrto Manolaki +1
Let be a closed subset of the unit circle of measure zero. Recently, Beise and Müller showed the existence of a function in the Hardy space for which the partial sums of…
Stable convergence of inner functions
Oleg Ivrii
Let be the set of inner functions whose derivative lies in the Nevanlinna class. In this paper, we discuss a natural topology on where if the…
On Makarov's principle in conformal mapping
Oleg Ivrii
We examine several characteristics of conformal maps that resemble the variance of a Gaussian: asymptotic variance, the constant in Makarov's law of iterated logarithm and the seco…