We discuss the relation between the growth of the resolvent near the unit circle and bounds for the powers of the operator. Resolvent conditions like those of Ritt and Kreiss are combined with growth conditions measuring the resolvent as a meromorphic function.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-2-2, author = {Olavi Nevanlinna}, title = {Resolvent conditions and powers of operators}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {113-134}, zbl = {0981.47002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-2-2} }
Olavi Nevanlinna. Resolvent conditions and powers of operators. Studia Mathematica, Tome 147 (2001) pp. 113-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-2-2/