TITLE:
Is –A-1 an Infinitesimal Generator?
AUTHORS:
Ru Liu
KEYWORDS:
α-Times Resolvent Family, Analytic α-Times Resolvent Family, Fractional Power of Generator
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.10,
October
10,
2018
ABSTRACT: There are some researchers considering the problem whether A-1 is the
generator of a bounded C0-semigroup
if A generates a bounded C0-semigroup. Actually, it is
a very basic and important problem. In this paper, we discuss whether -A-1 is the
generator of a bounded α-times
resolvent family if -A generates a
bounded α-times resolvent family.