264 research outputs found
Interpolation and harmonic majorants in big Hardy-Orlicz spaces
Free interpolation in Hardy spaces is caracterized by the well-known Carleson
condition. The result extends to Hardy-Orlicz spaces contained in the scale of
classical Hardy spaces , . For the Smirnov and the Nevanlinna
classes, interpolating sequences have been characterized in a recent paper in
terms of the existence of harmonic majorants (quasi-bounded in the case of the
Smirnov class). Since the Smirnov class can be regarded as the union over all
Hardy-Orlicz spaces associated with a so-called strongly convex function, it is
natural to ask how the condition changes from the Carleson condition in
classical Hardy spaces to harmonic majorants in the Smirnov class. The aim of
this paper is to narrow down this gap from the Smirnov class to ``big''
Hardy-Orlicz spaces. More precisely, we characterize interpolating sequences
for a class of Hardy-Orlicz spaces that carry an algebraic structure and that
are strictly bigger than . It turns out that the
interpolating sequences are again characterized by the existence of
quasi-bounded majorants, but now the weights of the majorants have to be in
suitable Orlicz spaces. The existence of harmonic majorants in such Orlicz
spaces will also be discussed in the general situation. We finish the paper
with an example of a separated Blaschke sequence that is interpolating for
certain Hardy-Orlicz spaces without being interpolating for slightly smaller
ones.Comment: 19 pages, 2 figure
Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums
We obtain asymptotic equalities for least upper bounds of deviations in the
uniform metric of de la Vall\'{e}e Poussin sums on the sets
C^{q}_{\beta}H_\omega of Poisson integrals of functions from the class H_\omega
generated by convex upwards moduli of continuity \omega(t) which satisfy the
condition \omega(t)/t\to\infty as t\to 0. As an implication, a solution of the
Kolmogorov-Nikol'skii problem for de la Vall\'{e}e Poussin sums on the sets of
Poisson integrals of functions belonging to Lipschitz classes H^\alpha,
0<\alpha <1, is obtaine
Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results
The chromosphere is a thin layer of the solar atmosphere that bridges the
relatively cool photosphere and the intensely heated transition region and
corona. Compressible and incompressible waves propagating through the
chromosphere can supply significant amounts of energy to the interface region
and corona. In recent years an abundance of high-resolution observations from
state-of-the-art facilities have provided new and exciting ways of
disentangling the characteristics of oscillatory phenomena propagating through
the dynamic chromosphere. Coupled with rapid advancements in
magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly
investigate the role waves play in supplying energy to sustain chromospheric
and coronal heating. Here, we review the recent progress made in
characterising, categorising and interpreting oscillations manifesting in the
solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review
The potential to encode sex, age, and individual identity in the alarm calls of three species of Marmotinae
In addition to encoding referential information and information about the sender’s motivation, mammalian alarm calls may encode information about other attributes of the sender, providing the potential for recognition among kin, mates, and neighbors. Here, we examined 96 speckled ground squirrels (Spermophilus suslicus), 100 yellow ground squirrels (Spermophilus fulvus) and 85 yellow-bellied marmots (Marmota flaviventris) to determine whether their alarm calls differed between species in their ability to encode information about the caller’s sex, age, and identity. Alarm calls were elicited by approaching individually identified animals in live-traps. We assume this experimental design modeled a naturally occurring predatory event, when receivers should acquire information about attributes of a caller from a single bout of alarm calls. In each species, variation that allows identification of the caller’s identity was greater than variation allowing identification of age or sex. We discuss these results in relation to each species’ biology and sociality
Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation, I. the least squares solution.
In this paper a state space formula is derived for the least squares solution X of the corona type Bezout equation G(z)X(z) =
Limb Spicules from the Ground and from Space
We amassed statistics for quiet-sun chromosphere spicules at the limb using
ground-based observations from the Swedish 1-m Solar Telescope on La Palma and
simultaneously from NASA's Transition Region and Coronal Explorer (TRACE)
spacecraft. The observations were obtained in July 2006. With the 0.2 arcsecond
resolution obtained after maximizing the ground-based resolution with the
Multi-Object Multi-Frame Blind Deconvolution (MOMFBD) program, we obtained
specific statistics for sizes and motions of over two dozen individual
spicules, based on movies compiled at 50-second cadence for the series of five
wavelengths observed in a very narrow band at H-alpha, on-band and in the red
and blue wings at 0.035 nm and 0.070 nm (10 s at each wavelength) using the
SOUP filter, and had simultaneous observations in the 160 nm EUV continuum from
TRACE. The MOMFBD restoration also automatically aligned the images,
facilitating the making of Dopplergrams at each off-band pair. We studied 40
H-alpha spicules, and 14 EUV spicules that overlapped H-alpha spicules; we
found that their dynamical and morphological properties fit into the framework
of several previous studies. From a preliminary comparison with spicule
theories, our observations are consistent with a reconnection mechanism for
spicule generation, and with UV spicules being a sheath region surrounding the
H-alpha spicules
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