Torture as a method of criminal prosecution: Police Brutality, the Militarization of Security and the Reform of Inquisitorial Criminal Justice in Mexico

How can societies restrain their coercive institutions and transition to a more humane criminal justice system? We argue that two main factors explain why torture can persist as a generalized practice in democratic societies: weak institutional protections of the rights of criminal suspects and the militarization of policing, which leads the police to act as if their job were to occupy a war zone. With the use of a large survey of the Mexican prison population and leveraging the date and place of arrest, this paper provides valid causal evidence about how these two explanatory variables shape torture. Our paper provides a grim picture of the survival of authoritarian policing practices in democracies. It also provides novel evidence of the extent to which the abolition of inquisitorial criminal justice institutions - a remnant of colonial legacies and a common trend in the region - has worked to restrain police brutality

A spectral radius type formula for approximation numbers of composition operators

For approximation numbers $a_n (C_\phi)$ of composition operators $C_\phi$ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol $\phi$ of uniform norm $< 1$, we prove that \lim_{n \to \infty} [a_n (C_\phi)]^{1/n} = \e^{- 1/ \capa [\phi (\D)]}, where \capa [\phi (\D)] is the Green capacity of \phi (\D) in \D. This formula holds also for $H^p$ with $1 \leq p < \infty$.Comment: 25 page

Estimates for approximation numbers of some classes of composition operators on the Hardy space

We give estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approximation numbers are dominated by \e^{- c \sqrt n}. When the symbol is continuous on the closed unit disk and has a domain touching the boundary non-tangentially at a finite number of points, with a good behavior at the boundary around those points, we can improve this upper estimate. A lower estimate is given when this symbol has a good radial behavior at some point. As an application we get that, for the cusp map, the approximation numbers are equivalent, up to constants, to \e^{- c \, n / \log n}, very near to the minimal value \e^{- c \, n}. We also see the limitations of our methods. To finish, we improve a result of O. El-Fallah, K. Kellay, M. Shabankhah and H. Youssfi, in showing that for every compact set $K$ of the unit circle \T with Lebesgue measure 0, there exists a compact composition operator $C_\phi \colon H^2 \to H^2$, which is in all Schatten classes, and such that $\phi = 1$ on $K$ and $|\phi | < 1$ outside $K$

Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk

We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the normalized area measure on the unit disk \D, by every analytic self-map \phi \colon \D \to \D is not only an $(\alpha + 2)$-Carleson measure, but that the measure of the Carleson windows of size \eps h is controlled by \eps^{\alpha + 2} times the measure of the corresponding window of size $h$. This means that the property of being an $(\alpha + 2)$-Carleson measure is true at all infinitesimal scales. We give an application by characterizing the compactness of composition operators on weighted Bergman-Orlicz spaces