Transfer functions and operator theory

Operator-valued Bergman Inner Functions as Transfer Functions

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...

Skew Toeplitz Theory and Pseudorational Transfer Functions

A state space version of the skew Toeplitz theory for (distributed) H" optimization theory is presented. The approach combines this theory with the realization theory for pseudorational transfer functions. 1 Time-Domain Interpretation of Sarason Space In [15], we established a strong link between the skew Toeplitz H" theory of 12, 4, 5, 6, 9, 121 and its realization in the time domain. The fund...

Operator Theory and Operator Algebras

Some Extensions of Loewner’s Theory of Monotone Operator Functions

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...

Operator and Spectral Theory

This lecture is a complete introduction to the general theory of operators on Hilbert spaces. We particularly focus on those tools that are essentials in Quantum Mechanics: unbounded operators, multiplication operators, self-adjointness, spectrum, functional calculus, spectral measures and von Neumann’s Spectral Theorem. 1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . ...