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Boundary relations

Abstracts 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 Herglotztype 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 A. Ran The nonsymmetric
discrete algebraic Riccati equation and canonical
factorization of rational matrix functions on the unit circle 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. [Back] 