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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-8, author = {M. C. Calder\'on-Moreno}, title = {Pseudo shift operators with large images}, journal = {Colloquium Mathematicae}, volume = {91}, year = {2002}, pages = {131-136}, zbl = {1017.30045}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-8} }
M. C. Calderón-Moreno. Pseudo shift operators with large images. Colloquium Mathematicae, Tome 91 (2002) pp. 131-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-1-8/