This volume is dedicated to the memory of Israel Glazman, an outstanding personality and distinguished mathematician, the author of many remarkable papers and books in operator theory and its applications. The present book opens with an essay devoted to Glazman's life and scientific achievements. It focusses on the areas of his unusually wide interests and consists of 18 mathematical papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, nonlinear functional analysis, approximation theory and optimization, and mathematical statistics. The book gives a picture of the current state of some important problems in areas of operator theory and its applications and will be of interest to a wide group of researchers working in pure and applied mathematics.
Table of ContentsIsrael Glazman, Mathematician and Personality.- Principle of Weakly Contractive Maps in Hilbert Spaces.- Potentials Associated to Rational Weights.- Multidimensional Functional Equations Generated by Affine Transformations.- Realization Theorems for Operator-Valued R-Functions.- Timan’s Type Result on Approximation by Algebraic Polynomials.- Asymptotic Formulas for Spectral and Weyl Functions of Sturm-Liouville Operators with Smooth Coefficients.- The Glazman-Krein-Naimark Theorem for Ordinary Differential Operators.- Metric Critical Point Theory 2. Deformation Techniques.- Ergodic Methods for the Construction of Holomorphic Retractions.- New Proof of Trace Formulas in Case of Classical Sturm-Liouville Problem.- Commuting Nonselfadjoint Operators and a Unified Theory of Waves and Corpuscles.- On Stability of Non-Negative Invariant Subspaces.- The Duality of Spectral Manifolds and Local Spectral Theory.- Degenerated Elliptic Boundary Value Problems for Weak Coupled Systems. Solvability and Maximum Principle.- Characterization of the Periodic and Anti-Periodic Spectra of Nonselfadjoint Hill’s Operators.- A Lower Confidence Limit for the Multiple Correlation Coefficient.- Analysis in Classes of Discontinuous Functions and Partial Differential Equations.- The Behaviour of Solutions of Ordinary Differential Equations in Infinite Domains.