9,853 research outputs found
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
Harmonic analysis of iterated function systems with overlap
In this paper we extend previous work on IFSs without overlap. Our method
involves systems of operators generalizing the more familiar Cuntz relations
from operator algebra theory, and from subband filter operators in signal
processing.Comment: 37 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
Ages, metallicities and -element enhancement for galaxies in Hickson compact groups
Central velocity dispersions and eight line-strength Lick indices have been
determined from 1.3 resolution long-slit spectra of 16 elliptical
galaxies in Hickson compact groups. These data were used to determine galaxy
properties (ages, metallicities and -element enhancements) and allowed
a comparison with the parameters determined for a sample of galaxies in lower
density environments, studied by Gonz\'alez (1993). The stellar population
parameters were derived by comparison to single stellar population models of
Thomas et al. (2003) and to a new set of SSP models for the indices Mg,
Fe5270 and Fe5335 based on synthetic spetra. These models, based on an update
version of the fitting functions presented in Barbuy et al. (2003), are fully
described here. Our main results are: (1) the two samples have similar mean
values for the metallicities and [/Fe] ratios, (2) the majority of the
galaxies in compact groups seem to be old (median age of 14 Gyr for eight
galaxies for which ages could be derived), in agreement with recent work by
Proctor et al. (2004). These findings support two possible scenarios: compact
groups are either young systems whose members have recently assembled and had
not enough time to experience any merging yet or, instead, they are old systems
that have avoided merging since their time of formation.Comment: Accepted for publication in A
An extension of Wiener integration with the use of operator theory
With the use of tensor product of Hilbert space, and a diagonalization
procedure from operator theory, we derive an approximation formula for a
general class of stochastic integrals. Further we establish a generalized
Fourier expansion for these stochastic integrals. In our extension, we
circumvent some of the limitations of the more widely used stochastic integral
due to Wiener and Ito, i.e., stochastic integration with respect to Brownian
motion. Finally we discuss the connection between the two approaches, as well
as a priori estimates and applications.Comment: 13 page
The NextGen Model Atmosphere grid: II. Spherically symmetric model atmospheres for giant stars with effective temperatures between 3000 and 6800~K
We present the extension of our NextGen model atmosphere grid to the regime
of giant stars. The input physics of the models presented here is nearly
identical to the NextGen dwarf atmosphere models, however spherical geometry is
used self-consistently in the model calculations (including the radiative
transfer). We re-visit the discussion of the effects of spherical geometry on
the structure of the atmospheres and the emitted spectra and discuss the
results of NLTE calculations for a few selected models.Comment: ApJ, in press (November 1999), 13 pages, also available at
http://dilbert.physast.uga.edu/~yeti/PAPERS and at
ftp://calvin.physast.uga.edu/pub/preprints/NG-giants.ps.g
First energetic neutral atom images from Polar
Energetic neutral atoms are created when energetic magnetospheric ions undergo charge exchange with cold neutral atoms in the Earth\u27s tenuous extended atmosphere (the geocorona). Since they are unaffected by the Earth\u27s magnetic field, these energetic neutrals travel away in straight line trajectories from the points of charge exchange. The remote detection of these particles provides a powerful means through which the global distribution and properties of the geocorona and ring current can be inferred. Due to its 2 Ă 9 RE polar orbit, the Polar spacecraft provides an excellent platform from which to observe ENAs because it spends much of its time in the polar caps which are usually free from the contaminating energetic charged particles that make observations of ENAs more difficult. In this brief report, we present the first ENA imaging results from Polar. Storm-time ENA images are presented for a northern polar cap apogee pass on August 29, 1996 and for a southern polar cap perigee pass on October 23, 1996. As well, we show with a third event (July 31, 1996) that ENA emissions can also be detected in association with individual substorm
Ola Bratteli and his diagrams
This article discusses the life and work of Professor Ola Bratteli
(1946--2015). Family, fellow students, his advisor, colleagues and coworkers
review aspects of his life and his outstanding mathematical accomplishments.Comment: 18 pages, 15 figure
Abusers of Clients of Women\u27s Shelter: Their Socialization and Resources
This is a study of men who abuse women. The respondents were residents of a shelter for battered wives during 1977-1978. The study assesses the effect of the abusers\u27 social resources and socialization experiences on their use of violence against the respondents. Abusers with military experience and criminal records used a greater number of different types of violence against their victims than their counterparts without these socialization experiences, and the relationships are specified by the abusers\u27 socioeconomic resources
The Fundamental Plane of Gravitational Lens Galaxies and The Evolution of Early-Type Galaxies in Low Density Environments
Most gravitational lenses are early-type galaxies in relatively low density
environments -- a ``field'' rather than a ``cluster'' population. We show that
field early-type galaxies with 0 < z < 1, as represented by the lens galaxies,
lie on the same fundamental plane as those in rich clusters at similar
redshifts. We then use the fundamental plane to measure the combined
evolutionary and K-corrections for early-type galaxies in the V, I and H bands.
Only for passively evolving stellar populations formed at z > 2 (H_0=65 km/s
Mpc, Omega_0=0.3, Lambda_0=0.7) can the lens galaxies be matched to the local
fundamental plane. The high formation epoch and the lack of significant
differences between the field and cluster populations contradict many current
models of the formation history of early-type galaxies. Lens galaxy colors and
the fundamental plane provide good photometric redshift estimates with an
empirical accuracy of -0.03 +/- 0.11 for the 17 lenses with known redshifts. A
mass model dominated by dark matter is more consistent with the data than
either an isotropic or radially anisotropic constant M/L mass model, and a
radially anisotropic model is better than an isotropic model.Comment: 36 pages, 9 figures, 6 tables. ApJ in press. Final version contains
more observational dat
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