# American Institute of Mathematical Sciences

March  2008, 7(2): 457-463. doi: 10.3934/cpaa.2008.7.457

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

 1 Department of Mathematics, University of California, Los Angeles, CA 90095, United States

Received  February 2007 Revised  July 2007 Published  December 2007

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.
Citation: Ciprian Preda. Discrete-time theorems for the dichotomy of one-parameter semigroups. Communications on Pure &amp; Applied Analysis, 2008, 7 (2) : 457-463. doi: 10.3934/cpaa.2008.7.457
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