A local Landau type inequality for semigroup orbits

Gerd Herzog, and Peer Christian Kunstmann. "A local Landau type inequality for semigroup orbits." Studia Mathematica 223.1 (2014): 19-26. <http://eudml.org/doc/285810>.

@article{GerdHerzog2014,
abstract = {Given a strongly continuous semigroup $(S(t))_\{t≥0\}$ on a Banach space X with generator A and an element f ∈ D(A²) satisfying $||S(t)f|| ≤ e^\{-ωt\}||f||$ and $||S(t)A²f|| ≤ e^\{-ωt\}||A²f||$ for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.},
author = {Gerd Herzog, Peer Christian Kunstmann},
journal = {Studia Mathematica},
keywords = {Landau inequality; strongly continuous semigroups},
language = {eng},
number = {1},
pages = {19-26},
title = {A local Landau type inequality for semigroup orbits},
url = {http://eudml.org/doc/285810},
volume = {223},
year = {2014},
}

TY - JOUR
AU - Gerd Herzog
AU - Peer Christian Kunstmann
TI - A local Landau type inequality for semigroup orbits
JO - Studia Mathematica
PY - 2014
VL - 223
IS - 1
SP - 19
EP - 26
AB - Given a strongly continuous semigroup $(S(t))_{t≥0}$ on a Banach space X with generator A and an element f ∈ D(A²) satisfying $||S(t)f|| ≤ e^{-ωt}||f||$ and $||S(t)A²f|| ≤ e^{-ωt}||A²f||$ for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.
LA - eng
KW - Landau inequality; strongly continuous semigroups
UR - http://eudml.org/doc/285810
ER -