Geodesic
On the growth of analytic semigroups along vertical lines
Studia Mathematica, Tome 138 (2000) no. 2, pp. 165-177
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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 
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José E. Galé;  . On the growth of analytic semigroups along vertical lines. Studia Mathematica, Tome 138 (2000) no. 2, pp. 165-177. doi: 10.4064/sm-138-2-165-177

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