2,627 research outputs found
An Approximation Problem in Multiplicatively Invariant Spaces
Let be Hilbert space and a -finite
measure space. Multiplicatively invariant (MI) spaces are closed subspaces of that are invariant under point-wise multiplication by
functions in a fix subset of Given a finite set of data
in this paper we prove the
existence and construct an MI space that best fits , in the
least squares sense. MI spaces are related to shift invariant (SI) spaces via a
fiberization map, which allows us to solve an approximation problem for SI
spaces in the context of locally compact abelian groups. On the other hand, we
introduce the notion of decomposable MI spaces (MI spaces that can be
decomposed into an orthogonal sum of MI subspaces) and solve the approximation
problem for the class of these spaces. Since SI spaces having extra invariance
are in one-to-one relation to decomposable MI spaces, we also solve our
approximation problem for this class of SI spaces. Finally we prove that
translation invariant spaces are in correspondence with totally decomposable MI
spaces.Comment: 18 pages, To appear in Contemporary Mathematic
Linear combinations of frame generators in systems of translates
A finitely generated shift invariant space is a closed subspace of
that is generated by the integer translates of a finite number of
functions. A set of frame generators for is a set of functions whose
integer translates form a frame for . In this note we give necessary and
sufficient conditions in order that a minimal set of frame generators can be
obtained by taking linear combinations of the given frame generators.
Surprisingly the results are very different to the recently studied case when
the property to be a frame is not required.Comment: 13 pages, To appear in J. Math. Anal. App
Weak-Scale Hidden Sector and Energy Transport in Fireball Models of Gamma-Ray Bursts
The annihilation of pairs of very weakly interacting particles in the
neibourghood of gamma-ray sources is introduced here as a plausible mechanism
to overcome the baryon load problem. This way we can explain how these very
high energy gamma-ray bursts can be powered at the onset of very energetic
events like supernovae (collapsars) explosions or coalescences of binary
neutron stars. Our approach uses the weak-scale hidden sector models in which
the Higgs sector of the standard model is extended to include a gauge singlet
that only interacts with the Higgs particle. These particles would be produced
either during the implosion of the red supergiant star core or at the aftermath
of a neutron star binary merger. The whole energetics and timescales of the
relativistic blast wave, the fireball, are reproduced.Comment: 4 pp, 1 ps fig, text revised and improve
Application of new measurement techniques and strategies to measure ammonia emissions from agricultural activities
Agriculture is the main contributor to the ammonia emissions in the Netherlands. In order to comply with the ammonia emission reduction assigned to the Netherlands, new techniques have been implemented to reduce the ammonia emissions from animal houses, and after application of slurry into the field
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