PRODUCT INTEGRATION ON TIME SCALES

We introduce the notion of product ∆-integral of a matrix function defined on an arbitrary time scale, and thus generalize the classical definition of product integral. We prove that every Riemann ∆-integrable matrix function is also product ∆-integrable, and investigate the properties of the indefinite product ∆-integral, including its relation to linear systems of dynamic equations. Finally, we generalize the notion of the matrix exponential function.