On the growth of analytic semigroups along vertical lines
Volume 138 / 2000
Studia Mathematica 138 (2000), 165-177
DOI: 10.4064/sm-138-2-165-177
Abstract
We construct two Banach algebras, one which contains analytic semigroups $(a^z)_{Re z>0}$ such that $|a^{1+iy}| → ∞$ arbitrarily slowly as $|y| → ∞$, the other which contains ones such that $|a^{1+iy}| → ∞$ arbitrarily fast
