20,885 research outputs found
Mostly Music: Nov. 24, 2002
Lyon Leifer, Shyam Kanehttps://neiudc.neiu.edu/mostlymusic/1038/thumbnail.jp
On certain Toeplitz operators and associated completely positive maps
We study Toeplitz operators with respect to a commuting -tuple of bounded
operators which satisfies some additional conditions coming from complex
geometry. Then we consider a particular such tuple on a function space. The
algebra of Toeplitz operators with respect to that particular tuple becomes
naturally homeomorphic to of a certain compact subset of . Dual Toeplitz operators are characterized. En route, we prove an
extension type theorem which is not only important for studying Toeplitz
operators, but also has an independent interest because dilation theorems do
not hold in general for .Comment: 25 pages. arXiv admin note: text overlap with arXiv:1706.0346
Non-harmonic -elliptic pseudo differential operators on manifolds
In this article, we introduce and study -elliptic pseudo-differential
operators in the framework of non-harmonic analysis of boundary value problems
on a manifold with boundary , introduced by Ruzhansky
and Tokmagambetov ( Int. Math. Res. Not. IMRN, (12), 3548-3615, 2016) in terms
of a model operator . More precisely, we consider a weighted
-symbol class
associated to a suitable weight function on a countable set
and study elements of the symbolic calculus for
pseudo-differential operators associated with -symbol class
by deriving formulae for the composition, adjoint,
and transpose. Using the notion of -ellipticity for symbols belonging to
-symbol class , we construct the
parametrix of -elliptic pseudo-differential operators. Further, we
investigate the minimal and maximal extensions for -elliptic
pseudo-differential operators and show that they coincide when the symbol
is -elliptic. We provide a necessary
and sufficient condition to ensure that the pseudo-differential operators
with symbol in the -symbol class is a compact operator in or a Riesz operator
in Finally, we prove G\"arding's inequality for
pseudo-differential operators associated with symbol from in the setting of non-harmonic analysis.Comment: 4
Hyperon production in near threshold nucleon-nucleon collisions
We study the mechanism of the associated Lambda-kaon and Sigma-kaon
production in nucleon-nucleon collisions over an extended range of near
threshold beam energies within an effective Lagrangian model, to understand of
the new data on pp --> p Lambda K+ and pp --> p Sigma0 K+ reactions published
recently by the COSY-11 collaboration. In this theory, the hyperon production
proceeds via the excitation of N*(1650), N*(1710), and N*(1720) baryonic
resonances. Interplay of the relative contributions of various resonances to
the cross sections, is discussed as a function of the beam energy over a larger
near threshold energy domain. Predictions of our model are given for the total
cross sections of pp --> p Sigma+K0, pp --> n Sigma+K+, and pn --> n Lambda K+
reactions.Comment: 16 pages, 4 figures, one new table added and dicussions are updated,
version accepted for publication by Physical Review
Strangeness production in proton-proton and proton-nucleus collisions
In these lectures we discuss the investigation of the strange meson
production in proton-proton () and in proton-nucleus () reactions
within an effective Lagrangian model. The kaon production proceeds mainly via
the excitations of (1650), (1710), and (1720) resonant
intermediate nucleonic states, in the collision of two initial state nucleons.
Therefore, the strangeness production is expected to provide information about
the resonances lying at higher excitation energies. For beam energies very
close to the kaon production threshold the hyperon-proton final state
interaction effects are quite important. Thus, these studies provide a check on
the models of hyperon-nucleon interactions. The in-medium production of kaons
show strong sensitivity to the self energies of the intermediate mesons.Comment: 16 pages, 9 figures, Talk presented in the workshop on Hadron
Physics, Puri, India, March 7-17,200
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