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Distortion growth for iterations of diffeomorphisms of the interval
Alexander Borichev
We obtain several results on the distortion asymptotics for the iterations of diffeomorphisms of the interval extending the recent work of Polterovich and Sodin.
Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index
Alexander Borichev, Hakan Hedenmalm, Alexander Volberg
In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition,…
Slow area-preserving diffeomorphisms of the torus
Alexander Borichev
We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.
Lower bounds for quasianalytic functions, II. The Bernstein quasianalytic functions
Alexander Borichev, Fedor Nazarov, Mikhail Sodin
Let F be a class of functions with the uniqueness property: if a function f in F vanishes on a set of positive measure, then f is the zero function. In many instances, we would lik…