A local Landau type inequality for semigroup orbits

Gerd Herzog; Peer Christian Kunstmann

Studia Mathematica, Tome 223 (2014), p. 19-26 / Harvested from The Polish Digital Mathematics Library

Résumé

Given a strongly continuous semigroup ${(S (t))}_{t \geq 0}$ on a Banach space X with generator A and an element f ∈ D(A²) satisfying $| | S (t) f | | \leq e^{- ω t} | | f | |$ and $| | S (t) A ² f | | \leq e^{- ω t} | | A ² f | |$ 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.

Publié le : 2014-01-01

Zbl 1302.47065

EUDML-ID : urn:eudml:doc:285810

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     title = {A local Landau type inequality for semigroup orbits},
     journal = {Studia Mathematica},
     volume = {223},
     year = {2014},
     pages = {19-26},
     zbl = {1302.47065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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) pp. 19-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-1-2/