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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator


Abstract

Found are conditions on a scalar type spectral operator $A$ in a complex Banach space necessary and sufficient for all weak solutions of the evolution equation \begin{equation*} y'(t)=Ay(t),\quad t\ge 0, \end{equation*} to be strongly Gevrey ultradifferentiable of order $\beta\ge 1$, in particular analytic or entire, on $[0,\infty)$. Certain inherent smoothness improvement effects are analyzed.

Key words: Weak solution, scalar type spectral operator, Gevrey classes.


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Article Information

TitleOn the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 4, 349-369
MilestonesReceived 12/07/2017
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 Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator, Methods Funct. Anal. Topology 24 (2018), no. 4, 349-369.


BibTex

@article {MFAT1114,
    AUTHOR = {Marat V. Markin},
     TITLE = {On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {349-369},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1114},
}


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