Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory

The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions, conservative discrete-time input/state/output linear systems, and $C_{\cdot 0}$ Hilbert-space contraction operators. We discuss an analogue of all these ideas in the context of weighted Hardy spaces over the unit disk and an associated class of hypercontraction operators

A Monte Carlo analysis of the liquid xenon TPC as gamma ray telescope

Extensive Monte Carlo modeling of a coded aperture x ray telescope based on a high resolution liquid xenon TPC has been performed. Results on efficiency, background reduction capability and source flux sensitivity are presented. We discuss in particular the development of a reconstruction algorithm for events with multiple interaction points. From the energy and spatial information, the kinematics of Compton scattering is used to identify and reduce background events, as well as to improve the detector response in the few MeV region. Assuming a spatial resolution of 1 mm RMS and an energy resolution of 4.5 percent FWHM at 1 MeV, the algorithm is capable of reducing by an order of magnitude the background rate expected at balloon altitude, thus significantly improving the telescope sensitivity