3,428 research outputs found
Wiener's theorem on hypergroups
The following theorem on the circle group T is due to Norbert Wiener: If f∈L1(T) has non-negative Fourier coefficients and is square integrable on a neighbourhood of the identity, then f∈L2(T). This result has been extended to even exponents including p=∞, but shown to fail for all other p∈(1,∞]. All of this was extended further (appropriately formulated) well beyond locally compact abelian groups. In this paper we prove Wiener's theorem for even exponents for a large class of commutative hypergroups. In addition, we present examples of commutative hypergroups for which, in sharp contrast to the group case, Wiener's theorem holds for all exponents p∈[1,∞]. For these hypergroups and the Bessel-Kingman hypergroup with parameter 12 we characterise those locally integrable functions that are of positive type and square-integrable near the identity in terms of amalgam spaces
The Broadband Afterglow of GRB980329
We present radio observations of the afterglow of the bright gamma-ray burst
GRB980329 made between one month and several years after the burst, a
re-analysis of previously published submillimeter data, and late-time optical
and near-infrared (NIR) observations of the host galaxy. From the absence of a
spectral break in the optical/NIR colors of the host galaxy, we exclude the
earlier suggestion that GRB980329 lies at a redshift of z >~5. We combine our
data with the numerous multi-wavelength observations of the early afterglow,
fit a comprehensive afterglow model to the entire broadband dataset, and derive
fundamental physical parameters of the blast-wave and its host environment.
Models for which the ejecta expand isotropically require both a high
circumburst density and extreme radiative losses from the shock. No low density
model (n << 10 cm^{-3}) fits the data. A burst with a total energy of ~ 10^{51}
erg, with the ejecta narrowly collimated to an opening angle of a few degrees,
driven into a surrounding medium with density ~ 20 cm^{-3}, provides a
satisfactory fit to the lightcurves over a range of redshifts.Comment: 27 pages, incl. 6 figures, minor revisions (e.g. added/updated
references) Accepted by Ap
Discovery of an Ultrasoft X-ray Transient Source in the 2XMM Catalog: a Tidal Disruption Event Candidate
We have discovered an ultrasoft X-ray transient source, 2XMMi
J184725.1-631724, which was detected serendipitously in two XMM-Newton
observations in the direction of the center of the galaxy IC 4765-f01-1504 at a
redshift of 0.0353. These two observations were separated by 211 days, with the
0.2-10 keV absorbed flux increasing by a factor of about 9. Their spectra are
best described by a model dominated by a thermal disk or a single-temperature
blackbody component (contributing >80% of the flux) plus a weak power-law
component. The thermal emission has a temperature of a few tens of eV, and the
weak power-law component has a photon index of ~3.5. Similar to the black hole
X-ray binaries in the thermal state, our source exhibits an accretion disk
whose luminosity appears to follow the relation. This would
indicate that the black hole mass is about 10^5-10^6 M_sun using the
best-fitting inner disk radius. Both XMM-Newton observations show variability
of about 21% on timescales of hours, which can be explained as due to fast
variations in the mass accretion rate. The source was not detected by ROSAT in
an observation in 1992, indicating a variability factor of >64 over longer
timescales. The source was not detected again in X-rays in a Swift observation
in 2011 February, implying a flux decrease by a factor of >12 since the last
XMM-Newton observation. The transient nature, in addition to the extreme
softness of the X-ray spectra and the inactivity of the galaxy implied by the
lack of strong optical emission lines, makes it a candidate tidal disruption
event. If this is the case, the first XMM-Newton observation would have been in
the rising phase, and the second one in the decay phase.Comment: 12 pages, 6 figures. Accepted for publication in Ap
Spectral Function of 2D Fermi Liquids
We show that the spectral function for single-particle excitations in a
two-dimensional Fermi liquid has Lorentzian shape in the low energy limit.
Landau quasi-particles have a uniquely defined spectral weight and a decay rate
which is much smaller than the quasi-particle energy. By contrast, perturbation
theory and the T-matrix approximation yield spurious deviations from Fermi
liquid behavior, which are particularly pronounced for a linearized dispersion
relation.Comment: 6 pages, LaTeX2e, 5 EPS figure
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