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/