Higher order dynamic equations on measure chains: Wronskians, disconjugacy, and interpolating families of functions

This paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations, which cover simultaneously as special cases (amo ng others) both differential equations and difference equations. We also de fine Markov. Fekete, and Descartes interpolating systems of functions. The main result of this paper states that disconjugacy is equivalent to the exi stence of any of the above interpolating systems of solutions and that it i s also equivalent to a certain factorization representation of the operator . The results in this paper unify the corresponding theories of disconjugac y for nth order linear ordinary differential equations and for nth order li near difference equations.