# A local Landau type inequality for semigroup orbits

Gerd Herzog; Peer Christian Kunstmann

Studia Mathematica (2014)

- Volume: 223, Issue: 1, page 19-26
- ISSN: 0039-3223

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topGerd 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 -

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