Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg-Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.Comment: 20 page

Review of scientific topics for Millimetron space observatory

This paper describes outstanding issues in astrophysics and cosmology that can be solved by astronomical observations in a broad spectral range from far infrared to millimeter wavelengths. The discussed problems related to the formation of stars and planets, galaxies and the interstellar medium, studies of black holes and the development of the cosmological model can be addressed by the planned space observatory Millimetron (the "Spectr-M" project) equipped with a cooled 10-m mirror. Millimetron can operate both as a single-dish telescope and as a part of a space-ground interferometer with very long baseline.Comment: The translation of the original article in Physics Uspekhi http://ufn.ru/ru/articles/2014/12/c

Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

Simulations of M87 and Sgr A* imaging with the Millimetron Space Observatory on near-Earth orbits

High resolution imaging of supermassive black holes shadows is a direct way to verify the theory of general relativity at extreme gravity conditions. Very Long Baseline Interferometry (VLBI) observations at millimeter/sub-millimeter wavelengths can provide such angular resolution for supermassive black holes, located in Sgr A* and M87. Recent VLBI observations of M87 with the Event Horizon Telescope (EHT) has shown such capabilities. The maximum obtainable spatial resolution of EHT is limited by Earth diameter and atmospheric phase variations. In order to improve the image resolution longer baselines are required. Radioastron space mission has successfully demonstrated the capabilities of Space-Earth VLBI with baselines much larger than Earth diameter. Millimetron is a next space mission of the Russian Space Agency that will operate at millimeter wavelengths. Nominal orbit of the observatory will be located around Lagrangian L2 point of the Sun-Earth system. In order to optimize the VLBI mode, we consider a possible second stage of the mission that could use near-Earth high elliptical orbit (HEO). In this contribution a set of near-Earth orbits is used for the synthetic space-ground VLBI observations of Sgr A* and M87 in joint Millimetron and EHT configuration. General-relativistic magnetohydrodynamic models (GRMHD) for black hole environment of Sgr A* and M87 are used for static and dynamic imaging simulations at 230 GHz. A comparison preformed between ground and space-ground baselines demonstrates that joint observations with Millimetron and EHT significantly improve the image resolution and allow the EHT+Millimetron to obtain snapshot images of Sgr A* probing dynamics at fast timescales.Comment: 12 pages, 6 figure