1,140 research outputs found
Families of spectral sets for Bernoulli convolutions
In this paper, we study the harmonic analysis of Bernoulli measures. We show
a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding
to certain Bernoulli measures, making use of contractive transfer operators.
For other cases, we exhibit maximal Fourier families that are not orthonormal
bases.Comment: 25 pages, same result
Additive spectra of the 1/4 Cantor measure
In this paper, we add to the characterization of the Fourier spectra for
Bernoulli convolution measures. These measures are supported on Cantor subsets
of the line. We prove that performing an odd additive translation to half the
canonical spectrum for the 1/4 Cantor measure always yields an alternate
spectrum. We call this set an additive spectrum. The proof works by connecting
the additive set to a spectrum formed by odd multiplicative scaling.Comment: 9 pages, 1 figur
Weyssenhoff fluid dynamics in general relativity using a 1+3 covariant approach
The Weyssenhoff fluid is a perfect fluid with spin where the spin of the
matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov
and Korotky showed that this fluid can be described as an effective fluid with
spin in general relativity. A dynamical analysis of such a fluid is performed
in a gauge invariant manner using the 1+3 covariant approach. This yields the
propagation and constraint equations for the set of dynamical variables. A
verification of these equations is performed for the special case of
irrotational flow with zero peculiar acceleration by evolving the constraints.Comment: 20 page
Scaling by 5 on a 1/4-Cantor Measure
Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one
associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In
the particular case where the scaling constant for the Cantor measure is 1/4
and two specific ONBs are selected for L^2(\mu), there is a unitary operator U
defined by mapping one ONB to the other. This paper focuses on the case in
which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor
measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper
states that the corresponding operator U is ergodic in the sense that only the
constant functions are fixed by U.Comment: 34 page
Analysis of unbounded operators and random motion
We study infinite weighted graphs with view to \textquotedblleft limits at
infinity,\textquotedblright or boundaries at infinity. Examples of such
weighted graphs arise in infinite (in practice, that means \textquotedblleft
very\textquotedblright large) networks of resistors, or in statistical
mechanics models for classical or quantum systems. But more generally our
analysis includes reproducing kernel Hilbert spaces and associated operators on
them. If is some infinite set of vertices or nodes, in applications the
essential ingredient going into the definition is a reproducing kernel Hilbert
space; it measures the differences of functions on evaluated on pairs of
points in . And the Hilbert norm-squared in will represent
a suitable measure of energy. Associated unbounded operators will define a
notion or dissipation, it can be a graph Laplacian, or a more abstract
unbounded Hermitian operator defined from the reproducing kernel Hilbert space
under study. We prove that there are two closed subspaces in reproducing kernel
Hilbert space which measure quantitative notions of limits at
infinity in , one generalizes finite-energy harmonic functions in
, and the other a deficiency index of a natural operator in
associated directly with the diffusion. We establish these
results in the abstract, and we offer examples and applications. Our results
are related to, but different from, potential theoretic notions of
\textquotedblleft boundaries\textquotedblright in more standard random walk
models. Comparisons are made.Comment: 38 pages, 4 tables, 3 figure
Detection of periodic signatures in the solar power spectrum. On the track of l=1 gravity modes
In the present work we show robust indications of the existence of g modes in
the Sun using 10 years of GOLF data. The present analysis is based on the
exploitation of the collective properties of the predicted low-frequency (25 to
140 microHz) g modes: their asymptotic nature, which implies a quasi
equidistant separation of their periods for a given angular degree (l). The
Power Spectrum (PS) of the Power Spectrum Density (PSD), reveals a significant
structure indicating the presence of features (peaks) in the PSD with near
equidistant periods corresponding to l=1 modes in the range n=-4 to n=-26. The
study of its statistical significance of this feature was fully undertaken and
complemented with Monte Carlo simulations. This structure has a confidence
level better than 99.86% not to be due to pure noise. Furthermore, a detailed
study of this structure suggests that the gravity modes have a much more
complex structure than the one initially expected (line-widths, magnetic
splittings...). Compared to the latest solar models, the obtained results tend
to favor a solar core rotating significantly faster than the rest of the
radiative zone. In the framework of the Phoebus group, we have also applied the
same methodology to other helioseismology instruments on board SoHO and ground
based networks.Comment: Proceedings of the SOHO-18/GONG2006/HELAS I: Beyond the spherical Su
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