In this book the authors develop a theory of free noncommutative functions, in both algebraic
and analytic settings. Such functions are defined as mappings from square matrices of all …

Generalized Schur functions are scalar-or operator-valued holomorphic functions such that
certain associated kernels have a finite number of negative squares. This book develops the …

Recently J. Agler studied the class S dof scalar-valued, analytic functions ofdcomplex
variablesffor whichf (T1,…, Td) has norm at most 1 for any collection ofdcommuting …

We study the relationship between power spectra of stationary stochastic inputs to a linear
filter and the corresponding state covariances, and identify the structure of positive …

Kre n space operator theory has long been a principal area of research in eastern
mathematics, and it is now enjoying a surge of interest in western countries as well. The …

Let U be a Hilbert space. By an ℒ (U)-valued positive analytic function on the open right half-
plane we mean an analytic function which satisfies the condition. This function need not be …

The state-covariance of a linear filter is characterized by a certain algebraic commutativity
property with the state matrix of the filter, and also imposes a generalized interpolation …

The class of ω-hyponormal operators is introduced. This class contains all p-hyponormal
operators. Certain properties of this class of operators are obtained. Among other things, it is …

In this paper we consider systems with the separable Hilbert inner, input and output spaces
X, N^-, N^+ of the form dx (t) dt= ̂ Bx (t)+ L φ^-(t), φ^+(t)= N (x (t), φ^-(t)), x (0)= a with some …

The one-to-one correspondence between one-dimensional linear (stationary, causal)
input/state/output systems and scattering systems with one evolution operator, in which the …