4,351 research outputs found
Frames, semi-frames, and Hilbert scales
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower)
semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently,
for an upper semi-frame, the frame operator is bounded, but has an unbounded
inverse, whereas a lower semi-frame has an unbounded frame operator, with
bounded inverse. For upper semi-frames, in the discrete and the continuous
case, we build two natural Hilbert scales which may yield a novel
characterization of certain function spaces of interest in signal processing.
We present some examples and, in addition, some results concerning the duality
between lower and upper semi-frames, as well as some generalizations, including
fusion semi-frames and Banach semi-frames.Comment: 27 pages; Numerical Functional Analysis and Optimization, 33 (2012)
in press. arXiv admin note: substantial text overlap with arXiv:1101.285
Unconditional convergence and invertibility of multipliers
In the present paper the unconditional convergence and the invertibility of
multipliers is investigated. Multipliers are operators created by (frame-like)
analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or
necessary conditions for unconditional convergence and invertibility are
determined depending on the properties of the analysis and synthesis sequences,
as well as the symbol. Examples which show that the given assertions cover
different classes of multipliers are given. If a multiplier is invertible, a
formula for the inverse operator is determined. The case when one of the
sequences is a Riesz basis is completely characterized.Comment: 31 pages; changes to previous version: 1.) the results from the
previous version are extended to the case of complex symbols m. 2.) new
statements about the unconditional convergence and boundedness are added
(3.1,3.2 and 3.3). 3.) the proof of a preliminary result (Prop. 2.2) was
moved to a conference proceedings [29]. 4.) Theorem 4.10. became more
detaile
Multipliers for p-Bessel sequences in Banach spaces
Multipliers have been recently introduced as operators for Bessel sequences
and frames in Hilbert spaces. These operators are defined by a fixed
multiplication pattern (the symbol) which is inserted between the analysis and
synthesis operators. In this paper, we will generalize the concept of Bessel
multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be
shown that bounded symbols lead to bounded operators. Symbols converging to
zero induce compact operators. Furthermore, we will give sufficient conditions
for multipliers to be nuclear operators. Finally, we will show the continuous
dependency of the multipliers on their parameters.Comment: 17 page
Analysis of the BATSE Continuous MER data
The CGRO/BATSE database includes many types of data such as the 16-channel
continuous background or medium energy resolution burst data (CONT and MER data
types). We have calculated some four hundred burst's medium energy resolution
spectra and Principal Component Analysis has been applied. We found five
components can describe GRBs' spectra.Comment: 4 pages, 2 figures, accepted in Nuovo Ciment
Discrete coherent states for higher Landau levels
We consider the quantum dynamics of a charged particle evolving under the
action of a constant homogeneous magnetic field, with emphasis on the discrete
subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2, R)
group (in the Hyperbolic case). We investigate completeness properties of
discrete coherent states associated with higher order Euclidean and hyperbolic
Landau levels, partially extending classic results of Perelomov and of
Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results
follow from identifying the completeness problem with known results from the
theory of Gabor frames. The results for the hyperbolic setting follow by using
a combination of methods from coherent states, time-scale analysis and the
theory of Fuchsian groups and their associated automorphic forms.Comment: Revised for Annals of Physic
A Principal Component Analysis of the 3B Gamma-Ray Burst Data
We have carried out a principal component analysis for 625 gamma-ray bursts
in the BATSE 3B catalog for which non-zero values exist for the nine measured
variables. This shows that only two out of the three basic quantities of
duration, peak flux and fluence are independent, even if this relation is
strongly affected by instrumental effects, and these two account for 91.6% of
the total information content. The next most important variable is the fluence
in the fourth energy channel (at energies above 320 keV). This has a larger
variance and is less correlated with the fluences in the remaining three
channels than the latter correlate among themselves. Thus a separate
consideration of the fourth channel, and increased attention on the related
hardness ratio appears useful for future studies. The analysis gives the
weights for the individual measurements needed to define a single duration,
peak flux and fluence. It also shows that, in logarithmic variables, the
hardness ratio is significantly correlated with peak flux, while is
significantly anticorrelated with peak flux. The principal component analysis
provides a potentially useful tool for estimating the improvement in
information content to be achieved by considering alternative variables or
performing various corrections on available measurementsComment: Ap.J., accepted 12/9/97; revised version contains a new appendix,
somewhat expanded discussion; latex, aaspp4, 15 page
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