Lorentz Center - Boundary relations from 14 Dec 2009 through 18 Dec 2009
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    Boundary relations
    from 14 Dec 2009 through 18 Dec 2009





Daniel Alpay

A new approach to linear stochastic systems


Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We present stability theorems for these systems. We also discuss state space theory. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior. The talk is based on joint works with David Levanony and Ariel Pinhas.



Michael A. Dritschel

Realization techniques for obtaining a bounded functional calculus for certain sectorial operators


We sketch a way of using the realization theorem to get a bounded functional for Hilbert space operators whose imaginary powers are bounded when the powers lie in an interval of the real line, so giving a result along the lines of McIntosh's theorem for operators with bounded imaginary powers.  Included are a Herglotz-type representation and transfer function representation.  We also indicate how these results might be extended to the multivariable case.



K.-H.F. Förster

Factorizations of nonnegative operators and their extremal nonnegative extensions

Abstract Förster



A. Ran

The non-symmetric discrete algebraic Riccati equation and canonical factorization of rational matrix functions on the unit circle

Abstract Ran



J. Zemanek

Fixed points of holomorphic mappings


In this joint work with Simeon Reich and David Shoikhet, we study the structure of the fixed point set of a holomorphic mapping defined on a (not necessarily bounded) domain in a complex Banach space, by means of ergodic theory and a nonlinear numerical range.