3 papers
math.CV2007
On the "pits effect" of Littlewood and Offord
Alexandre Eremenko, Iossif Ostrovskii
Suppose that the moduli of the coefficients of a power series are 1/n!, while the arguments are arbitrary. If an entire function f represented by such power series decreases expone…
math.CA2001
The Hilbert transform, rearrangements, and logarithmic determinants
V. Matsaev, I. Ostrovskii, M. Sodin
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
math.CV2000
Variations on the theme of Marcinkiewicz' inequality
V. Matsaev, I. Ostrovskii, M. Sodin
We present a new approach to the Marcinkiewicz interpolation inequality for the distribution function of the Hilbert transform, and prove an "abstract" version of this inequality.…