Adjustment of the electric charge and current in pulsar magnetospheres

We present a simple numerical model of the plasma flow within the open field line tube in the pulsar magnetosphere. We study how the plasma screens the rotationally induced electric field and maintains the electric current demanded by the global structure of the magnetosphere. We show that even though bulk of the plasma moves outwards with relativistic velocities, a small fraction of particles is continuously redirected back forming reverse plasma flows. The density and composition (positrons or electrons, or both) of these reverse flows are determined by the distribution of the Goldreich-Julian charge density along the tube and by the global magnetospheric current. These reverse flows could significantly affect the process of the pair plasma production in the polar cap accelerator. Our simulations also show that formation of the reverse flows is accompanied by the generation of long wavelength plasma oscillations, which could be converted, via the induced scattering on the bulk plasma flow, into the observed radio emission.Comment: 24 pages, 11 figure

Sampling of Entire Functions of Several Complex Variables on a Lattice and Multivariate Gabor Frames

We give a general construction of entire functions in $d$ complex variables that vanish on a lattice of the form $L = A (Z + i Z )^d$ for an invertible complex-valued matrix. As an application we exhibit a class of lattices of density >1 that fail to be a sampling set for the Bargmann-Fock space in $C ^2$. By using an equivalent real-variable formulation, we show that these lattices fail to generate a Gabor frame

Riesz bases of reproducing kernels in Fock type spaces

In a scale of Fock spaces $\mathcal F_\varphi$ with radial weights $\varphi$ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if $\varphi(x)$ grows at most like $(\log x)^2$.Comment: 14 page

Uncertainty Principles and Vector Quantization

Given a frame in C^n which satisfies a form of the uncertainty principle (as introduced by Candes and Tao), it is shown how to quickly convert the frame representation of every vector into a more robust Kashin's representation whose coefficients all have the smallest possible dynamic range O(1/\sqrt{n}). The information tends to spread evenly among these coefficients. As a consequence, Kashin's representations have a great power for reduction of errors in their coefficients, including coefficient losses and distortions.Comment: Final version, to appear in IEEE Trans. Information Theory. Introduction updated, minor inaccuracies corrected

Radial oscillation of harmonic functions in the Korenblum class

We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class. We prove that functions which admit two-sided Korenblum estimate either oscillate or have slow growth along almost all radii

Frame Constants of Gabor Frames near the Critical Density

We consider Gabor frames generated by a Gaussian function and describe the behavior of the frame constants as the density of the lattice approaches the critical value