Inverses of generators of nonanalytic semigroups

• Autorzy: Ralph deLaubenfels
• Języki publikacji: EN

Abstrakty

EN

Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup ${e^{tA}}_{t≥0}$. It is shown that $A^{-1}$ generates an $O(1+τ) A(1 - A)^{-1}$-regularized semigroup. Several equivalences for $A^{-1}$ generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of ${e^{tA}}_{t≥0}$, on subspaces, for $A^{-1}$ generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate a strongly continuous semigroup. We also show that, for k a natural number, if ${e^{tA}}_{t≥0}$ is exponentially stable, then $||e^{τA^{-1}}x|| = O(τ^{1/4-k/2})$ for $x ∈ 𝓓(A^{k})$.

Kategorie tematyczne

• 47D03: Groups and semigroups of linear operators
• 47A60: Functional calculus
• 47D60: C -semigroups, regularized semigroups
• 47D62: Integrated semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 1
• Strony: 11-38

Daty

wydano

2009

Twórcy

autor

Ralph deLaubenfels

• 1841 Drew Avenue, Columbus, OH 43235, U.S.A.
• Department of Mathematics, Ohio State University, Columbus, OH 43210, U.S.A.

Identyfikatory

DOI

10.4064/sm191-1-2