The Characteristic Operator Function and Related Topics

This volume contains translations of six of the original papers of Moshe Livsic on the characteristic operator function, together with a collection of contributions devoted to Moshe Livsic’s theory of the characteristic operator function and its impact on the spectral analysis of non-selfadjoint operators, a theory first introduced in the 1940s. This theory provides a framework for the spectral analysis of non-selfadjoint and non-unitary operators and has since become a cornerstone of modern operator theory. Over the past seventy-five years, Livsic’s theory has exerted a lasting influence on analysis, complex analysis, linear systems theory, and a broad range of related topics. The volume examines how Livsic’s theory has shaped the study of pairs of commuting operators, a research direction initiated in the early 1970s with the aim of linking systems theory, non-selfadjoint operator theory, and Riemannian geometry. The contributions collected here reflect the scope and depth of Livsic’s work at the intersection of operator theory, geometry, and systems theory. This book will be a valuable resource for researchers and advanced graduate students working in operator theory, analysis, systems theory and related areas. A number of recollections from colleagues, students and friends of Moshe Livsic are also included.