A local Landau type inequality for semigroup orbits

• Autorzy: Gerd Herzog , Peer Christian Kunstmann
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 223
• Numer: 1
• Strony: 19-26

Daty

wydano

2014

Twórcy

autor

Gerd Herzog

• Karlsruhe Institute of Technology (KIT), Institute for Analysis, Kaiserstr. 89, D-76128 Karlsruhe, Germany

autor

Peer Christian Kunstmann

• Karlsruhe Institute of Technology (KIT), Institute for Analysis, Kaiserstr. 89, D-76128 Karlsruhe, Germany

Identyfikatory

DOI

10.4064/sm223-1-2