Factorization method on time scales

Abstract: We present an approach to the factorization method for second order difference equations on time scales. We construct Hilbert spaces of functions on the time scale and show how to construct a chain of intertwined first order $\Delta$-difference operators $\mathcal A_k$ in the sense that $\mathcal A_k$ and $\mathcal A_k^*$ act as ladder operators generating new solutions of eigenproblem of $\mathcal A_k\mathcal A_k^*$.