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 $b$ is an inner function, then composition with $b$ induces an endomorphism, $\beta$, of $L^\infty(\mathbb{T})$ that leaves $H^\infty(\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\mathbb{T}))$ and $B(H^2(\mathbb{T}))$ that implement $\beta$ through the representations of $L^\infty(\mathbb{T})$ and $H^\infty(\mathbb{T})$ in terms of multiplication operators on $L^2(\mathbb{T})$ and $H^2(\mathbb{T})$. 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 $C^*$-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