Structure and reorientation kinetics of hydrogen passivated shallow impurities in silicon from vibrational spectroscopy

A survey is presented of what has been learned from vibrational spectroscopy and theory about the structure and reorientation kinetics of hydrogen-passivated shallow impurities in Si.     

Nonlinear Filtering for Diffusions in Random Environments

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X ^W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Filter products of C0-semigroups and ultraproduct representations for Lie groups

We provide a new approach to filter products of C₀-semigroups and prove a spectral theorem for the generator and its filter product. In a similar fashion, we construct ultraproducts of strongly continuous unitary representations of locally compact groups and study spectral theoretic connections between the representations and their ultraproducts. In the case of Lie groups, our investigations are extended to the infinitesimal representation.