The umbral transfer-matrix method. I. Foundations

Abstract

We lay the foundations for the Umbral Transfer-Matrix Method, based on Gian-Carlo Rota's seminal notion of the "umbra" as a linear functional on a vector space of formal power series. The full potential of Rota's concept, to be described in subsequent parts of this series of articles, emerges when it is implemented on a computer. © 2000 Academic Press.