18,902 research outputs found
Characterization of almost -eigenfunctions of the Laplace-Beltrami operator
In \cite{Roe} Roe proved that if a doubly-infinite sequence of
functions on satisfies and for
all and , then where
and are real constants. This result was extended to by
Strichartz \cite{Str} where is substituted by the Laplacian on .
While it is plausible to extend this theorem for other Riemannian manifolds or
Lie groups, Strichartz showed that the result holds true for Heisenberg groups,
but fails for hyperbolic 3-space. This negative result can be indeed extended
to any Riemannian symmetric space of noncompact type. We observe that this
failure is rooted in the -dependance of the -spectrum of the Laplacian
on the hyperbolic spaces. Taking this into account we shall prove that for all
rank one Riemannian symmetric spaces of noncompact type, or more generally for
the harmonic groups, the theorem actually holds true when uniform
boundedness is replaced by uniform "almost boundedness". In addition we
shall see that for the symmetric spaces this theorem is capable of
characterizing the Poisson transforms of functions on the boundary, which
some what resembles the original theorem of Roe on .Comment: 30 page
Anisotropic cosmological models with two fluids
In this paper, aniostropic dark energy cosmological models have been
constructed in a Bianchi-V space-time with the energy momentum tensor
consisting of two non-interacting fluids namely bulk viscous fluid and dark
energy fluid. Two different models are constructed based on the power law
cosmology and de Sitter universe. The constructed model also embedded with
different pressure gradients along different spatial directions. The variable
equation of state (EoS) parameter, skewness parameters for both the models are
obtained and analyzed. The physical properties of the models obtained with the
use of scale factors of power law and de Sitter law are also presented.Comment: 10 pages, 12 figure
Possible existence of wormholes in the galactic halo region
Two observational results, the density profile from simulations performed in
the CDM scenario and the observed flat galactic rotation curves, are
taken as input with the aim of showing that the galactic halo possesses some of
the characteristics needed to support traversable wormholes. This result should
be sufficient to provide an incentive for scientists to seek observational
evidence for wormholes in the galactic halo region.Comment: 11 pages, 3 figures, 1 table, Eur. Phys. J. C (2014) 74:2750, DOI
10.1140/epjc/s10052-014-2750-
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