9,147 research outputs found
On the Schatten-von Neumann properties of some pseudo-differential operators
We obtain a number of explicit estimates for quasi-norms of
pseudo-differential operators in the Schatten-von Neumann classes with
. The estimates are applied to derive semi-classical bounds for
operators with smooth or non-smooth symbols.Comment: 22 page
Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains
We prove a two-term quasi-classical trace asymptotic formula for the
functions of multi-dimensional Wiener-Hopf operators with discontinuous
symbols. The discontinuities occur on the surfaces which are assumed to be
piece-wise smooth. Such a two-term formula was conjectured by H. Widom in 1982,
and proved by A. V Sobolev for smooth surfaces in 2009.Comment: 15 page
On a coefficient in trace formulas for Wiener-Hopf operators
Let be a smooth function quickly decreasing at
infinity. For the Wiener-Hopf operator with the symbol , and a smooth
function , H. Widom in 1982 established the following
trace formula: where is given explicitly in terms of
the functions and . The paper analyses the coefficient for a class of non-smooth functions assuming that is real-valued. A
representative example of one such function is with some
.Comment: 21 page
Maser action in methanol transitions
We report the detection with the ATCA of 6.7 GHz methanol emission towards
OMC-1. The source has a size between 40'' and 90'', is located to the
south-east of Ori-KL and may coincide in position with the 25 GHz masers. The
source may be an example of an interesting case recently predicted in theory
where the transitions of traditionally different methanol maser classes show
maser activity simultaneously. In addition, results of recent search for
methanol masers from the 25 and 104.3 GHz transitions are reported.Comment: To appear in the Proceedings of the 2004 European Workshop: "Dense
Molecular Gas around Protostars and in Galactic Nuclei", Eds. Y.Hagiwara,
W.A.Baan, H.J. van Langevelde, 2004, a special issue of ApSS, Kluwer; author
list has been corrected, text is unchange
Stochastic Schrodinger equations as limit of discrete filtering
We consider an open model possessing a Markovian quantum stochastic limit and
derive the limit stochastic Schrodinger equations for the wave function
conditioned on indirect observations using only the von Neumann projection
postulate. We show that the diffusion (Gaussian) situation is universal as a
result of the central limit theorem with the quantum jump (Poissonian)
situation being an exceptional case. It is shown that, starting from the
correponding limiting open systems dynamics, the theory of quantum filtering
leads to the same equations, therefore establishing consistency of the quantum
stochastic approach for limiting Markovian models.Comment: 21 pages, no figure
DISTRIBUTION OF INTEGER LATTICE POINTS IN A BALL CENTRED AT A DIOPHANTINE POINT
We study the variance of the fluctuations in the number of lattice points in a ball and in a thin spherical shell of large radius centred at a Diophantine point
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