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Infinitesimal generators of invertible evolution families


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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TitleInfinitesimal generators of invertible evolution families
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 1, 26-36
MathSciNet   MR3632386
zbMATH 06810665
Milestones  Received 31/10/2016; Revised 17/12/2016
CopyrightThe Author(s) 2017 (CC BY-SA)

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

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


@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},
  MRNUMBER = {MR3632386},
 ZBLNUMBER = {06810665},
       URL = {},


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