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.
Table of Contents:
Part I Translations.- 1. On an Application of the Theory of Hermitian Operators to the Generalized Moment Problem by M.S. Livshits.- 2. A Theorem on the Multiplication of Characteristic Matrix-Functions by M.S. Livshits.- 3. The Application of Non-Self-Adjoint Operators to Scattering Theory by M.S. Livshits.- 4. On Linear Physical Systems Connected with the External World by Coupling Channels by M.S. Livshits.- 5. Open Systems as Linear Automata by M.S. Livshits.- 6. Open Geometry and Operator Colligations by L.L. Vaksman and M.S. Livshits.- Part II Research paper.- 7. Characteristic Function of M.S. Livsic and Triangular Models of Bounded Linear Operators by Vladimir K. Dubovoy, Bernd Kirstein, Conrad Madler and Karsten Mueller.- 8. Characteristic Function, Schur Interpolation Problem and Darlington Synthesis by Sergey S. Boiko,Vladimir K. Dubovoy,Bernd Fritzsche,Bernd Kirstein,Conrad Madler and Karsten Mueller.- 9. Characteristic Function, Schur Parameters and Pseudocontinuation of Schur Functions by Vladimir K. Dubovoy,Bernd Fritzsche,Bernd Kirstein,Conrad Madler and Karsten Mueller.- 10. Characteristic Function of M. Livsic and some Developments by Lev Sakhnovich.- 11. The Sine Kernel, Two Corresponding Operator Identities, and Random Matrices by Lev Sakhnovich.- 12. Characteristic Function of Pencils. Model Representations of a Quadratic Operator Pencil by V.A. Zolotarev.- Part III Recollections.- 13. M.S. Livsic (1917–2007) by V.A. Marchenko,E.R. Tsekanovski,V.K. Dubovoy and V.A. Zolotarev.- 14. The Bravery of a Scientist by B.S. Pavlov.- 15. M.S. Livsic (1917–2007) L.L. Vaksman (1951–2007) by V.K. Dubovoy, V.A. Zolotarev, A.A. Yantsevich and A.G. Rutkas.
