We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.

The problem of stabilizing a linear control system leads to several important considerations. In particular, there are certain basic requirements which need to satisfied in any practical feedback system [6, 7, 11, 18]. First, the closed-loop system needs to be internally stable, i.e., the transfer function between any two points in the loop should be stable. Internal stability guarantees that a...

Allan Borodin of the University of Toronto has been awarded the 2008 CRMFields-PIMS prize. According to the citation “Professor Borodin is a world leader in the mathematical foundations of computer science. His influence on theoretical computer science has been enormous, and its scope very broad. Jon Kleinberg, winner of the 2006 Nevanlinna Prize, writes of Borodin, “he is one of the few resear...

We provide a comprehensive analysis of matrix-valued Herglotz functions and illustrate their applications in the spectral theory of self-adjoint Hamiltonian systems including matrix-valued Schrödinger and Dirac-type operators. Special emphasis is devoted to appropriate matrix-valued extensions of the well-known Aronszajn-Donoghue theory concerning support properties of measures in their Nevanli...

We consider the problem of generating a matrix transfer function with prescribed strict bistability, biproperness, and positivity properties from a sequence of positive definite sample values at points on the frequency axis. We show how this arises in problems from multi-input/multioutput control analysis and design. This is a matrix interpolation problem with additional conditions, both on the...

Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to useful tool for solving various problems control theory and electrical engineering. Over the years many extensions of original problem were considered, including different function spaces, nonstationary problems, several variable settings with matrix operator points. Here we discuss variation on positive real ...