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A spectral countability condition for almost automorphy of solutions of differential equations |
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| Authors: | Nguyen Van Minh Toshiki Naito Gaston Nguerekata |
| Affiliation: | Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118 ; Department of Mathematics, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan ; Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, Maryland 21251 |
| Abstract: | We consider the almost automorphy of bounded mild solutions to equations of the form   -periodic  and almost automorphic  in a Banach space  . Under the assumption that  does not contain  , the part of the spectrum of the monodromy operator associated with the evolutionary process generated by  on the unit circle is countable. We prove that every bounded mild solution of  on the real line is almost automorphic. |
| Keywords: | Evolution equation mild solution almost automorphy uniform spectrum |
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