991 research outputs found
A lower bound in Nehari's theorem on the polydisc
By theorems of Ferguson and Lacey (d=2) and Lacey and Terwilleger (d>2),
Nehari's theorem is known to hold on the polydisc D^d for d>1, i.e., if H_\psi
is a bounded Hankel form on H^2(D^d) with analytic symbol \psi, then there is a
function \phi in L^\infty(\T^d) such that \psi is the Riesz projection of \phi.
A method proposed in Helson's last paper is used to show that the constant C_d
in the estimate \|\phi\|_\infty\le C_d \|H_\psi\| grows at least exponentially
with d; it follows that there is no analogue of Nehari's theorem on the
infinite-dimensional polydisc
Von Bezold assimilation effect reverses in stereoscopic conditions
Lightness contrast and lightness assimilation are opposite phenomena: in contrast,
grey targets appear darker when bordering bright surfaces (inducers) rather than dark ones; in
assimilation, the opposite occurs. The question is: which visual process favours the occurrence
of one phenomenon over the other? Researchers provided three answers to this question. The
first asserts that both phenomena are caused by peripheral processes; the second attributes their
occurrence to central processes; and the third claims that contrast involves central processes,
whilst assimilation involves peripheral ones. To test these hypotheses, an experiment on an IT
system equipped with goggles for stereo vision was run. Observers were asked to evaluate the
lightness of a grey target, and two variables were systematically manipulated: (i) the apparent
distance of the inducers; and (ii) brightness of the inducers. The retinal stimulation was kept
constant throughout, so that the peripheral processes remained the same. The results show that
the lightness of the target depends on both variables. As the retinal stimulation was kept constant, we
conclude that central mechanisms are involved in both lightness contrast and lightness assimilation
Multiplication and Composition in Weighted Modulation Spaces
We study the existence of the product of two weighted modulation spaces. For
this purpose we discuss two different strategies. The more simple one allows
transparent proofs in various situations. However, our second method allows a
closer look onto associated norm inequalities under restrictions in the Fourier
image. This will give us the opportunity to treat the boundedness of
composition operators.Comment: 49 page
Composition Operators and Endomorphisms
If is an inner function, then composition with induces an
endomorphism, , of that leaves
invariant. We investigate the structure of the
endomorphisms of and that implement
through the representations of and
in terms of multiplication operators on
and . Our analysis, which is based on work
of R. Rochberg and J. McDonald, will wind its way through the theory of
composition operators on spaces of analytic functions to recent work on Cuntz
families of isometries and Hilbert -modules
The Dirichlet-to-Robin Transform
A simple transformation converts a solution of a partial differential
equation with a Dirichlet boundary condition to a function satisfying a Robin
(generalized Neumann) condition. In the simplest cases this observation enables
the exact construction of the Green functions for the wave, heat, and
Schrodinger problems with a Robin boundary condition. The resulting physical
picture is that the field can exchange energy with the boundary, and a delayed
reflection from the boundary results. In more general situations the method
allows at least approximate and local construction of the appropriate reflected
solutions, and hence a "classical path" analysis of the Green functions and the
associated spectral information. By this method we solve the wave equation on
an interval with one Robin and one Dirichlet endpoint, and thence derive
several variants of a Gutzwiller-type expansion for the density of eigenvalues.
The variants are consistent except for an interesting subtlety of
distributional convergence that affects only the neighborhood of zero in the
frequency variable.Comment: 31 pages, 5 figures; RevTe
Does wage rank affect employees' well-being?
How do workers make wage comparisons? Both an experimental study and an analysis of 16,000 British employees are reported. Satisfaction and well-being levels are shown to depend on more than simple relative pay. They depend upon the ordinal rank of an individual's wage within a comparison group. “Rank” itself thus seems to matter to human beings. Moreover, consistent with psychological theory, quits in a workplace are correlated with pay distribution skewness
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