6 papers
How to Bake a Composition Operator from Scratch
Michael R Pilla
At face value, composition operators look like something first experienced in algebra. It's just composition of functions after all. However, there is a deep and technical setting…
Rhaly-Type Operators in Several Complex Variables
Michael R. Pilla
Recently, a generalization of the Cesàro operator to several variables was introduced as a tuple acting on the Drury-Arveson space \cite{P}. We determine the norm of these Cesàro-t…
Cesàro-Type Operators Acting on the Drury-Arveson Space
Michael R. Pilla
The celebrated Cesàro operator is a well-known operator with interesting connections to a variety of objects in operator theory. Generalizations have been made for Cesàro-type oper…
Linear Fractional Self-Maps of the Unit Ball in
Michael R. Pilla
Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining…
One Parameter Semigroups in Two Complex Variables
Michael R. Pilla
For self maps of the disk, it can be shown that under the right conditions one can embed a discrete iteration of the map into a continuous semigroup. In this article we extend thes…
A Generalized Cross Ratio
Michael R. Pilla
In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In par…