ON UNIFORM POLYNOMIAL TRISPLITTING OF EVOLUTION OPERATORS

Claudia Luminita Mihiț^†, Ghiocel Moț^‡

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.

Keywords: evolution operators, polynomial trisplitting, polynomial trichotomy.

MSC: 34D05, 34D09.

DOI  10.56082/annalsarscimath.2026.3.145

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^*Accepted for publication on July 28, 2026
^†claudia.mihit@uav.ro, Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania
^‡ghiocel.mot@uav.ro, Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997