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On the mean ergodicity of weak solutions of an abstract evolution equation


Abstract

Found are conditions of rather general nature sufficient for the existence of the limit at infinity of the Cesàro means $$ \frac{1}{t} \int_0^ty(s)\,ds $$ for every bounded weak solution $y(\cdot)$ of the abstract evolution equation $$ y'(t)=Ay(t),\ t\ge 0, $$ with a closed linear operator $A$ in a Banach space $X$.

Key words: Mean ergodicity, weak solution.


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Article Information

TitleOn the mean ergodicity of weak solutions of an abstract evolution equation
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 53-70
MilestonesReceived 10/03/2017; Revised 03/09/2017
CopyrightThe Author(s) 2018 (CC BY-SA)

Authors Information

Marat V. Markin
Department of Mathematics, California State University, Fresno, 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA


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Citation Example

Marat V. Markin, On the mean ergodicity of weak solutions of an abstract evolution equation, Methods Funct. Anal. Topology 24 (2018), no. 1, 53-70.


BibTex

@article {MFAT1025,
    AUTHOR = {Marat V. Markin},
     TITLE = {On the mean ergodicity of weak solutions of an abstract evolution equation},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {53-70},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1025},
}


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