1,561,646 research outputs found
Renormings of
We investigate the best order of smoothness of . We prove in
particular that there exists a -smooth bump function on if
and only if and are both even integers and is a multiple of .Comment: 18 pages; AMS-Te
On -- trace inequalities
We give necessary and sufficient conditions in order that inequalities of the
type hold for a class of integral operators with nonnegative kernels, and measures and
on , in the case where and .
An important model is provided by the dyadic integral operator with kernel
, where
is the family of all dyadic cubes in , and are
arbitrary nonnegative constants associated with .
The corresponding continuous versions are deduced from their dyadic
counterparts. In particular, we show that, for the convolution operator with positive radially decreasing kernel , the trace
inequality holds if and only if , where
. Here is a nonlinear Wolff
potential defined by and
. Analogous inequalities for
were characterized earlier by the authors using a different method
which is not applicable when
A Riemann Hypothesis for characteristic p L-functions
We propose analogs of the classical Generalized Riemann Hypothesis and the
Generalized Simplicity Conjecture for the characteristic p L-series associated
to function fields over a finite field. These analogs are based on the use of
absolute values. Further we use absolute values to give similar reformulations
of the classical conjectures (with, perhaps, finitely many exceptional zeroes).
We show how both sets of conjectures behave in remarkably similar ways.Comment: This is the final version (with new title) as it will appear in the
Journal of Number Theor
- estimates for Electromagnetic Helmholtz equation
In space dimension , we consider the electromagnetic Schr\"odinger
Hamiltonian and the corresponding Helmholtz equation
. We extend the well known
- estimates for the solution of the free Helmholtz equation to the
case when the electromagnetic hamiltonian is considered.Comment: 13 pages, 3 figure
The Mid-Infrared Period-Luminosity Relations for the Small Magellanic Cloud Cepheids Derived from Spitzer Archival Data
In this paper we derive the Spitzer IRAC band period-luminosity (P-L)
relations for the Small Magellanic Cloud (SMC) Cepheids, by matching the
Spitzer archival SAGE-SMC data with the OGLE-III SMC Cepheids. We find that the
3.6micron and 4.5micron band P-L relations can be better described using two
P-L relations with a break period at log(P)=0.4: this is consistent with
similar results at optical wavelengths for SMC P-L relations. The 5.8micron and
8.0micron band P-L relations do not extend to sufficiently short periods to
enable a similar detection of a slope change at log(P)=0.4. The slopes of the
SMC P-L relations, for log(P)>0.4, are consistent with their LMC counterparts
that were derived from a similar dataset. They are also in agreement with those
obtained from a small sample of Galactic Cepheids with parallax measurements.Comment: 14 pages, 5 figures and 2 tables. ApJ accepte
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