Bounded operators on weighted spaces of holomorphic functions on the polydisk

We consider the weighted $A^p(\omega)$ and $B_p(\omega)$ spaces of holomorphic functions on the polydisk (in the case of $p>1$). We prove some theorems about the boundedness of Toeplitz operators on weighted Besov spaces $B_p(\omega)$ and about the boundedness of generalized little Hankel and Berezin- type operators on $A^p(\omega)$.Comment: 1

A principal possibility for computer investigation of evolution of dynamical systems with independent on time accuracy

Extensive N-body simulations are among the key means for the study of numerous astrophysical and cosmological phenomena, so various schemes are developed for possibly higher accuracy computations. We demonstrate the principal possibility for revealing the evolution of a perturbed Hamiltonian system with an accuracy independent on time. The method is based on the Laplace transform and the derivation and analytical solution of an evolution equation in the phase space for the resolvent and using computer algebra.Comment: Eur Phys Journ C (in press), to match the version to appear, 7 pages, 3 fig

A new exactly integrable hypergeometric potential for the Schr\"odinger equation

We introduce a new exactly integrable potential for the Schr\"odinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions. This is a potential step with variable height and steepness. We present the general solution of the problem, discuss the transmission of a quantum particle above the barrier, and derive explicit expressions for the reflection and transmission coefficients

Holomorphic Bloch spaces on the unit ball in CnC^n

summary:This work is an introduction to anisotropic spaces of holomorphic functions, which have $\omega$-weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding $L_\omega ^\infty$ space. We establish a description of $(A^p(\omega ))^*$ via the Bloch classes for all $0<p\leq 1$

Supernova 2002ic: the collapse of a stripped-envelope, massive star in a dense medium ?

We revisit the case of SN2002ic that recently revived the debate about the progenitors of SNeIa after the claim of the unprecedented presence of hydrogen lines over a diluted SNIa spectrum. As an alternative to the previous interpretation, we suggest that SN2002ic actually was a type Ic SN, the core collapse of a massive star which lost its hydrogen and helium envelope. In this scenario the observed interaction with a dense circumstellar material (CSM) is the predictable consequence of the intense mass-loss of the progenitor and/or of the presence of a gas rich environment. With this view we establish a link between energetic SNeIc and highly interacting SNeIIn and add some credits to the proposed association of some SNeIIn to GRBs.Comment: Accepted for publication on ApJ