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    STUDIA MATHEMATICA - Issue no. 3 / 2014  
         
  Article:   ON A CLASS OF DICHOTOMOUS EVOLUTION OPERATORS WITH STRONGLY CONTINUOUS FAMILIES OF PROJECTIONS.

Authors:  .
 
       
         
  Abstract:   The aim of this paper is to present a concept of nonuniform exponential dichotomy through a certain class of strongly continuous evolution operators defi ned with the aid of a particular family of projections acting on the state space.This class easily emphasizes the fact that, in the case of uniform exponential dichotomy, the uniform exponential growth is essential in order to prove the boundedness of the dichotomic family of projections. The main result of the paper is the extension of the boundedness result in the nonuniform setting.

Mathematics Subject Classi fication (2010): 34D09.

Keywords: nonuniform exponential dichotomy, strongly continuous families of projections, strongly continuous evolution operators.
 
         
     
         
         
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