Communications on Pure and Applied Analysis (CPAA)

Discrete-time theorems for the dichotomy of one-parameter semigroups

Pages: 457 - 463, Volume 7, Issue 2, March 2008      doi:10.3934/cpaa.2008.7.457

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Ciprian Preda - Department of Mathematics, University of California, Los Angeles, CA 90095, United States (email)

Abstract: Discrete-time sufficient conditions for the dichotomy of $C_0$-semigroups are obtained in the general case when it is not required that the kernel of the dichotomic projector to be $T(t)$-invariant. Thus are extended known results due to Datko, Pazy, Zabczyk.

Keywords:  One-parameter semigroup, dichotomy.
Mathematics Subject Classification:  34D09, 47D06.

Received: February 2007;      Revised: July 2007;      Available Online: December 2007.