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A local Landau type inequality for semigroup orbits

100%

Herzog G., Kunstmann P.

Studia Mathematica

2014

tom 223

nr 1

19-26

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.

Classes of distribution semigroups

81%

Kunstmann P., Mijatović M., Pilipović S.

Studia Mathematica

2008

tom 187

nr 1

37-58

We introduce various classes of distribution semigroups distinguished by their behavior at the origin. We relate them to quasi-distribution semigroups and integrated semigroups. A class of such semigroups, called strong distribution semigroups, is characterized through the value at the origin in the sense of Łojasiewicz. It contains smooth distribution semigroups as a subclass. Moreover, the analysis of the behavior at the origin involves intrinsic structural results for semigroups. To this purpose, new test function spaces and distribution semigroups over these spaces are introduced. We give applications to Schrödinger type equations in the spaces $C_{b}$, $L^{∞}$, and BMO with elliptic non-densely defined operators.

Ograniczanie wyników

2 Studia Mathematica

2 Kunstmann P.

1 Herzog G.

1 Mijatović M.

1 Pilipović S.

1 2014

1 2008

Wyniki wyszukiwania

A local Landau type inequality for semigroup orbits

Classes of distribution semigroups