Why the Riesz transforms are averages of the dyadic shifts?

The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators -so-called dyadic shifts. We show here that the same is true in any $\mathbb{R}^n$ -the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new one

Similarity of operators and geometry of eigenvector bundles

We characterize the contractions that are similar to the backward shift in the Hardy space H². This characterization is given in terms of the geometry of the eigenvector bundles of the operators

Why the Riesz transforms are averages of the dyadic shifts?

The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators -so-called dyadic shifts. We show here that the same is true in any Rn -the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new one

Oxidation and Cross-Linking in the Curing of Air-Drying Artists' Oil Paints

In this study, the chemistry of air-drying artist's oil paint curing and aging up to 24 months was studied. The objective is to improve our molecular understating of the processes that lead to the conversion of the fluid binder into a dry film and how this evolves with time, which is at the base of a better comprehension of degradation phenomena of oil paintings and relevant to the artists' paint manufacturing industry. To this aim, a methodological approach based on thermogravimetric (TG) analysis, differential scanning calorimetry (DSC), gas chromatography-mass spectrometry (GC-MS), and analytical pyrolysis coupled with gas chromatography and mass spectrometry (Py-GC-MS) was implemented. Model paintings based on linseed oil and safflower oil (a drying and a semidrying oil, respectively) mixed with two historically relevant pigments - lead white (a through drier) and synthetic ultramarine blue (a pigment often encountered in degraded painting layers) - were investigated. The oil curing under accelerated conditions (80 °C under air flow) was followed by isothermal TG analysis. The oxygen uptake profiles were fit by a semiempiric equation that allowed to study the kinetics of the oil oxidation and estimate oxidative degradation. The DSC signal due to hydroperoxide decomposition and radical recombination was used to monitor the radical activity over time and to evaluate the stability of peroxides formed in the paint layers. GC-MS was performed at 7 and 24 months of natural aging to investigate the noncovalently cross-linked fractions and Py-GC-MS to characterize the whole organic fraction of the model paintings, including the cross-linked network. We show that the oil-pigment combination may have a strong influence on the relative degree of oxidation of the films formed with respect to its degree of cross-linking, which may be correlated with the literature on the stability of painting layers. Undocumented pathways of oxidation are also highlighted

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

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) =