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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.

### Article Information

 Title On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 4, 349-369 MathSciNet MR3912070 Milestones Received 12/07/2017 Copyright The 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

### 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},
MRNUMBER = {MR3912070},
URL = {http://mfat.imath.kiev.ua/article/?id=1114},
}

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