Anders Olofsson

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 discrete time linear systems. This points to a new interaction between the fields of invariant subspace theory and mathematical systems theory.

A representation formula for radially weighted biharmonic functions in the unit disc

Let

Characterizations of Bergman space Toeplitz operators with harmonic symbols

w\colon \mathbb{D}\to(0,\infty)

A computation of Poisson kernels for some standard weighted biharmonic operators in the unit disc

be a radial continuous weight function. We consider the weighted biharmonic equation \Delta w^{-1}\Delta u=0\quad\text{in } \mathbb{D} with Dirichlet boundary conditions

Behavior at infinity of solutions of an equation of Osserman–Keller type☆

u = f_0

An operator inequality for weighted Bergman shift operators

and

A characteristic operator function for the class of n-hypercontractions

\partial_n u = f_1

Wandering Subspace Theorems

on

An Operator-valued Berezin Transform and the Class of n-Hypercontractions

\mathbb{T} = \partial\mathbb{D}

Differential operators for a scale of Poisson type kernels in the unit disc

. Under some extra conditions on the weight function