A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces

We consider the cubic Nonlinear Schrodinger Equation in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time H^s bounds in terms of the H^s size of the initial data for s greater than or equal to -1/6.Comment: 27 pages very minor misprints corrected (see formulas (4), (7)

Dispersive estimates for principally normal pseudodifferential operators

The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials.Comment: 72 page

The Case for Limited Auditor Liability - The Effects of Liability Size on Risk Aversion and Ambiguity Aversion

Both the US and the EU consider limiting auditor liability in order to ensure the viability of the audit market, but fear its potentially negative impact on audit quality. Our paper discusses the existing empirical results on this topic in the auditing and behavioral economics literature, and provides new evidence based on a controlled laboratory experiment. Our experiment involves real losses and allows for direct inference of behaviour under limited and unlimited liability in situations of ambiguous liability risk. Our findings imply that limited liability can induce an efficient level of audit effort, while unlimited liability induces an inefficiently high level of audit effort. This paper contributes to the literature on auditor liability, as well behavioral economics research in general, by addressing recent controversial issues on behavior in the presence of ambiguity and real losses.

Sharp L^p bounds on spectral clusters for Lipschitz metrics

We establish L^p bounds on L^2 normalized spectral clusters for self-adjoint elliptic Dirichlet forms with Lipschitz coefficients. In two dimensions we obtain best possible bounds for all p between $2 and infinity, up to logarithmic losses for$6<p\leq 8$. In higher dimensions we obtain best possible bounds for a limited range of p.Comment: 28 page