A locally connected continuum without convergent sequences

We answer a question of Juhasz by constructing under CH an example of a locally connected continuum without nontrivial convergent sequences.Comment: 6 pages. Reprinted from Topology and its Applications, in press, Jan van Mill, A locally connected continuum without convergent sequence

Player identification in American McGee’s Alice : a comparative perspective

In this paper I analyse personal identification in three incarnations of Alice in Wonderland: the original novels, the 1950s Disney animation film and the computer game American McGee’s Alice. After presenting the research corpus, I lay out the analytical framework derived from Kendall Walton’s theory of representational artefacts as props for evoking imagining in games of make-believe. From this perspective, the Alice heritage relies on spectacle rather than plot to entertain. This spectacle differs across media as each medium’s strengths are played out: language-play in the novels, colour/motion/sound in the film and challenges in the game. There are two types of imagining involved: objective, whereby a person imagines a scene outside of himself, and subjective, in which case the imagining revolves around a version of himself. Both the novels and the film primarily evoke objective imagining whereas the game invites the player to be introjected into the Alice character evoking subjective imagining. The picture is not unambiguous, however, as the novels and the film stage a broad array of subjectifying techniques and the game objectifying ones. This gives us some indication as to the nature of representation which, to be of interest, presents a tension between here and there, between the self and an other

The L^p-Poincar\'e inequality for analytic Ornstein-Uhlenbeck operators

Consider the linear stochastic evolution equation dU(t) = AU(t) + dW_H(t), t\ge 0, where A generates a C_0-semigroup on a Banach space E and W_H is a cylindrical Brownian motion in a continuously embedded Hilbert subspace H of E. Under the assumption that the solutions to this equation admit an invariant measure \mu_\infty we prove that if the associated Ornstein-Uhlenbeck semigroup is analytic and has compact resolvent, then the Poincar\'e inequality \n f - \overline f\n_{L^p(E,\mu_\infty)} \le \n D_H f\n_{L^p(E,\mu_\infty)} holds for all 1<p<\infty. Here \overline f denotes the average of f with respect to \mu_\infty and D_H the Fr\'echet derivative in the direction of H.Comment: Minor correctiopns. To appear in the proceedings of the symposium "Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics", June 2013, Herrnhut, German

Poisson stochastic integration in Banach spaces

We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone representation formula.Comment: 26 page

Non-tangential maximal functions and conical square functions with respect to the Gaussian measure

We study, in $L^{1}(\R^n;\gamma)$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some extent, to compensate for the non-doubling character of the gaussian measure. The main result asserts that conical square functions can be controlled in $L^1$-norm by non-tangential maximal functions. Along the way we prove a change of aperture result for the latter. This complements recent results on gaussian Hardy spaces due to Mauceri and Meda.Comment: 21 pages, revised version with various arguments simplified and generalise