Given a strongly continuous semigroup $(S(t))_{t\ge0}$ on
a Banach space $X$ with generator $A$ and an element $f\in D(A^2)$
satisfying $\|S(t)f\|\le e^{-\omega t}\|f\|$ and
$\|S(t)A^2f\|$$\le e^{-\omega t}\|A^2f\|$ for all $t\ge0$ and some $\omega>0$,
we derive a Landau type inequality for $\|Af\|$ in terms of $\|f\|$ and $\|A^2f\|$. This inequality improves on the usual Landau inequality that holds in the case $\omega=0$.
@article{10_4064_sm223_1_2,
author = {Gerd Herzog and Peer Christian Kunstmann},
title = {A local {Landau} type inequality for semigroup orbits},
journal = {Studia Mathematica},
pages = {19--26},
year = {2014},
volume = {223},
number = {1},
doi = {10.4064/sm223-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm223-1-2/}
}
TY - JOUR
AU - Gerd Herzog
AU - Peer Christian Kunstmann
TI - A local Landau type inequality for semigroup orbits
JO - Studia Mathematica
PY - 2014
SP - 19
EP - 26
VL - 223
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm223-1-2/
DO - 10.4064/sm223-1-2
LA - en
ID - 10_4064_sm223_1_2
ER -
%0 Journal Article
%A Gerd Herzog
%A Peer Christian Kunstmann
%T A local Landau type inequality for semigroup orbits
%J Studia Mathematica
%D 2014
%P 19-26
%V 223
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm223-1-2/
%R 10.4064/sm223-1-2
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Gerd Herzog; Peer Christian Kunstmann. A local Landau type inequality for semigroup orbits. Studia Mathematica, Tome 223 (2014) no. 1, pp. 19-26. doi: 10.4064/sm223-1-2
