Is $A^{-1}$ an infinitesimal generator?

• Autorzy: Hans Zwart
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the question whether $A^{-1}$ is the infinitesimal generator of a bounded C₀-semigroup if A generates a bounded C₀-semigroup. If the semigroup generated by A is analytic and sectorially bounded, then the same holds for the semigroup generated by $A^{-1}$. However, we construct a contraction semigroup with growth bound minus infinity for which $A^{-1}$ does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its inverse does not generate a semigroup. Hence we show that the question posed by deLaubenfels in [13] must be answered negatively. All these examples are on Banach spaces. On a Hilbert space the question whether the inverse of a generator of a bounded semigroup also generates a bounded semigroup still remains open.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 93C25: Systems in abstract spaces
• 46N40: Applications in numerical analysis
• 47D60: C -semigroups, regularized semigroups
• 93D20: Asymptotic stability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 75
• Numer: 1
• Strony: 303-313

Daty

wydano

2007

Twórcy

autor

Hans Zwart

• Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

Identyfikatory

DOI

10.4064/bc75-0-18