ON UNIFORM POLYNOMIAL TRISPLITTING OF EVOLUTION OPERATORS*

Source abstract

The article explores the concept of uniform polynomial trisplitting, as generalization of the uniform polynomial trichotomy for the case of evolution operators in Banach spaces. We prove that the uniform polynomial trisplitting in continuous-time is equivalent to the uniform polynomial trisplitting in discrete-time (assuming the existence of the uniform polynomial growth), using compatible families of projections, respectively strongly compatible families of projections. Also, discrete criteria for this property are given and in particular, new results for uniform polynomial trichotomy are obtained.