Kernel behaviors on time scales

Abstract

This paper is a first attempt to introduce the behavioral approach into dynamical systems define on a time scale. The notion of kernel behavior on a time scale as the kernel of a delta differential matrix operator is introduced. Basic properties, as surjectivity and injectivity, of this operator are studied. A characterization of equivalent kernel representations is given. Additionally, the question whether a behavior that admits a representation with auxiliary variables is also a kernel behavior is analyzed.