Pseudo shift operators with large images
Volume 93 / 2002
Colloquium Mathematicum 93 (2002), 131-136
MSC: Primary 30E10; Secondary 47B37.
DOI: 10.4064/cm93-1-8
Abstract
We give suitable conditions for the existence of many holomorphic functions $f$ on a disc such that the image of any nonempty open subset under the action of pseudo shift operators on $f$ is arbitrarily large. This generalizes an earlier result about images of derivatives and completes another one on infinite order differential operators.
