4 papers
Asymptotics of the Fourier and Laplace transforms in weighted spaces of analytic functions
Vladimir Matsaev, Mikhail Sodin
We study the asymptotics near the origin of the Fourier transform in weighted Hardy spaces of analytic functions in the upper half-plane, and of the Laplace transform in weighted s…
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.
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.…
Entire functions and compact operators with -imaginary component
Vladimir Matsaev, Mikhail Sodin
We study operators of the form X+Y where Y has a finite p-th Schatten norm (p<2), and X is self-adjoint and of Hilbert-Schmidt class. Our study is based on new theorems on zero dis…