Electron. J. Diff. Eqns., Vol. 2008(2008), No. 21, pp. 1-18.

Almost automorphic functions with values in p-Frechet spaces

Ciprian G. Gal, Sorin G. Gal, Gaston M. N'Guerekata

Abstract:
In this paper we develop a theory of almost automorphic functions with values in p-Frechet spaces, $0<p<1$, including the $l^{p}$, $L^{p}$ spaces and the Hardy space $H^{p}$. Although the p-norm for $0<p<1$ does not have all the properties of an usual norm, the majority of main properties of almost automorphic functions with values in Banach spaces are extended to this case. Applications to semigroups of linear operators and to dynamical systems in p-Frechet spaces are given.

Submitted December 19, 2007. Published February 21, 2008.
Math Subject Classifications: 43A60, 34C35.
Key Words: Almost automorphic; asymptotically almost automorphic; weakly almost automorphic; semigroup of linear bounded operator; p-Frechet space.

Show me the PDF file (313 KB), TEX file for this article.

Ciprian G. Gal
Department of Mathematics
University of Missouri
Columbia, MO 65211, USA
email: ciprian@math.missouri.edu
Sorin G. Gal
Department of Mathematics and Computer Science
University of Oradea
410087 Oradea, Romania
email: galso@uoradea.ro
Gaston M. N'Guérékata
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu

Return to the EJDE web page