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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.

### Article Information

 Title Infinitesimal generators of invertible evolution families Source Methods Funct. Anal. Topology, Vol. 23 (2017), no. 1, 26-36 MathSciNet MR3632386 zbMATH 06810665 Milestones Received 31/10/2016; Revised 17/12/2016 Copyright The 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

### 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},
MRNUMBER = {MR3632386},
ZBLNUMBER = {06810665},
URL = {http://mfat.imath.kiev.ua/article/?id=944},
}

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