Is –A-1 an Infinitesimal Generator? - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.10, October 2018

Is –A^-1 an Infinitesimal Generator? ()

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DOI: 10.4236/jamp.2018.610169 425 Downloads 855 Views Citations

Author(s)

Ru Liu

Affiliation(s)

College of Information Science and Engineering, Chengdu University, Chengdu, China.

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.

KEYWORDS

α-Times Resolvent Family, Analytic α-Times Resolvent Family, Fractional Power of Generator

Share and Cite:

Liu, R. (2018) Is –A^-1 an Infinitesimal Generator?. Journal of Applied Mathematics and Physics, 6, 1979-1987. doi: 10.4236/jamp.2018.610169.

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