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Infinitesimal generators of invertible evolution families


Abstract

A logarithm representation of operators is introduced as well as a concept of pre-infinitesimal generator. Generators of invertible evolution families are represented by the logarithm representation, and a set of operators represented by the logarithm is shown to be associated with analytic semigroups. Consequently generally-unbounded infinitesimal generators of invertible evolution families are characterized by a convergent power series representation.

Key words: Invertible evolution family, operator theory, maximal regularity.


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Article Information

TitleInfinitesimal generators of invertible evolution families
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 1, 26–36
MilestonesReceived 31/10/2016; Revised 17/12/2016
CopyrightThe Author(s) 2017 (CC BY-SA)

Authors Information

Yoritaka Iwata
Institute of Innovative Research, Tokyo Institute of Technology; Department of Mathematics, Shibaura Institute of Technology


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Citation Example

Yoritaka Iwata, Infinitesimal generators of invertible evolution families, Methods Funct. Anal. Topology 23 (2017), no. 1, 26–36.


BibTex

@article {MFAT944,
    AUTHOR = {Iwata, Yoritaka},
     TITLE = {Infinitesimal generators of invertible evolution families},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {23},
      YEAR = {2017},
    NUMBER = {1},
     PAGES = {26–36},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=944},
}


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