Fractional Functions and their Representations

Abstract

For arbitrary non-identically zero functions f , we will introduce some natural fractional functions f1 having f as denominators and we shall consider their representations f1 by appropriate numerator functions within a reproducing kernel Hilbert spaces framework. That is, in the present work we would like to introduce very general fractional functions (e.g., having the possibility of admitting zeros in their denominators) by means of the theory of reproducing kernels.