This book presents English translations of Michele Sce's most important works, originally written in Italian during the period 1955-1973, on hypercomplex analysis and algebras of hypercomplex numbers. Despite their importance, these works are not very well known in the mathematics community because of the language they were published in. Possibly the most remarkable instance is the so-called Fueter-Sce mapping theorem, which is a cornerstone of modern hypercomplex analysis, and is not yet understood in its full generality.

This volume is dedicated to revealing and describing the framework Sce worked in, at an exciting time when the various generalizations of complex analysis in one variable were still in their infancy. In addition to faithfully translating Sce's papers, the authors discuss their significance and explain their connections to contemporary research in hypercomplex analysis. They also discuss many concrete examples that can serve as a basis for further research.

The vast majority of the results presented here will be new to readers, allowing them to finally access the original sources with the benefit of comments from fellow mathematicians active in the field of hypercomplex analysis. As such, the book offers not only an important chapter in the history of hypercomplex analysis, but also a roadmap for further exciting research in the field.

Provides a unique account of Sce's work in the context of the modern development of the theory of hypercomplex variables Presents English translations of Sce's papers that are otherwise hard to find Includes old, very deep results that are not known to a wide readership Written in a style that will appeal to a wide audience

Autorentext

Daniel Alpay, Foster G. and Mary McGaw Professorship in Mathematical Sciences, Chapman University Fabrizio Colombo is professor at the Politecnico di Milano, Italy. Irene Sabadini is professor at the Politecnico di Milano, Italy.

Inhalt
1 Introduction.- 2 Monogenicity and total derivability in real and complex algebras.- 3 On systems of partial differential equations related to real algebras.- 4 On the variety of zero divisors in algebras.- 5 Remarks on the power series in quadratic modules.- 6 Regular functions in the Cayley algebra.- Index.