metric spaces and critical values of smooth functions.

"The notions of transfer function and characteristic functions proved to be fundamental in the last fifty years in operator theory and in system theory. Moshe Livsic played a central role in developing these notions, and the book contains a selection of carefully chosen refereed papers dedicated to his memory. Topics include classical operator theory, ergodic theory and stochastic processes, geometry of smooth mappings, mathematical physics, Schur analysis and system theory. The variety of topics attests well to the breadth of Moshe Livsic's mathematical vision and the deep impact of his work.The book will appeal to researchers in mathematics, electrical engineering and physics."

Differential-difference Equations in Entire Functions.- Inverse Stieltjes-like Functions and Inverse Problems for Systems with Schrödinger Operator.- Bi-Isometries and Commutant Lifting.- The One-sided Ergodic Hilbert Transform of Normal Contractions.- Model Reduction in Symbolically Semi-separable Systems with Application to Pre-conditioners for 3D Sparse Systems of Equations.- Pick Matrices for Schur Multipliers.- The Stable Rank of a Nest Algebra and Strong Stabilization of Linear Time-varying Systems.- Convexity of Ranges and Connectedness of Level Sets of Quadratic Forms.- The Schur Algorithm in Terms of System Realizations.- On Some Interrelations Between J-Potapov Functions and J-Potapov Sequences.- A Solvable Model for Scattering on a Junction and a Modified Analytic Perturbation Procedure.- Integral Equations in the Theory of Levy Processes.- ?-spread of Sets in Metric Spaces and Critical Values of Smooth Functions.