Ebook: New Results in Operator Theory and Its Applications: The Israel M. Glazman Memorial Volume

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.

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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.

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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.
Content:
Front Matter....Pages I-VII
Israel Glazman, Mathematician and Personality....Pages 1-6
Principle of Weakly Contractive Maps in Hilbert Spaces....Pages 7-22
Potentials Associated to Rational Weights....Pages 23-40
Multidimensional Functional Equations Generated by Affine Transformations....Pages 41-54
Realization Theorems for Operator-Valued R-Functions....Pages 55-91
Timan’s Type Result on Approximation by Algebraic Polynomials....Pages 92-101
Asymptotic Formulas for Spectral and Weyl Functions of Sturm-Liouville Operators With Smooth Coefficients....Pages 102-117
The Glazman-Krein-Naimark Theorem for Ordinary Differential Operators....Pages 118-130
Metric Critical Point Theory 2. Deformation Techniques....Pages 131-144
Ergodic Methods for the Construction of Holomorphic Retractions....Pages 145-152
New Proof of Trace Formulas in Case of Classical Sturm-Liouville Problem....Pages 153-162
Commuting Nonselfadjoint Operators and a Unified Theory of Waves and Corpuscles....Pages 163-185
On Stability of Non-Negative Invariant Subspaces....Pages 186-189
The Duality of Spectral Manifolds and Local Spectral Theory....Pages 190-207
Degenerated Elliptic Boundary Value Problems for Weak Coupled Systems. Solvability and Maximum Principle....Pages 208-215
Characterization of the Periodic and Anti-Periodic Spectra of Nonselfadjoint Hill’s Operators....Pages 216-224
A Lower Confidence Limit for the Multiple Correlation Coefficient....Pages 225-229
Analysis in Classes of Discontinuous Functions and Partial Differential Equations....Pages 230-248
The Behaviour of Solutions of Ordinary Differential Equations in Infinite Domains....Pages 249-257
Back Matter....Pages 258-261

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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.
Content:
Front Matter....Pages I-VII
Israel Glazman, Mathematician and Personality....Pages 1-6
Principle of Weakly Contractive Maps in Hilbert Spaces....Pages 7-22
Potentials Associated to Rational Weights....Pages 23-40
Multidimensional Functional Equations Generated by Affine Transformations....Pages 41-54
Realization Theorems for Operator-Valued R-Functions....Pages 55-91
Timan’s Type Result on Approximation by Algebraic Polynomials....Pages 92-101
Asymptotic Formulas for Spectral and Weyl Functions of Sturm-Liouville Operators With Smooth Coefficients....Pages 102-117
The Glazman-Krein-Naimark Theorem for Ordinary Differential Operators....Pages 118-130
Metric Critical Point Theory 2. Deformation Techniques....Pages 131-144
Ergodic Methods for the Construction of Holomorphic Retractions....Pages 145-152
New Proof of Trace Formulas in Case of Classical Sturm-Liouville Problem....Pages 153-162
Commuting Nonselfadjoint Operators and a Unified Theory of Waves and Corpuscles....Pages 163-185
On Stability of Non-Negative Invariant Subspaces....Pages 186-189
The Duality of Spectral Manifolds and Local Spectral Theory....Pages 190-207
Degenerated Elliptic Boundary Value Problems for Weak Coupled Systems. Solvability and Maximum Principle....Pages 208-215
Characterization of the Periodic and Anti-Periodic Spectra of Nonselfadjoint Hill’s Operators....Pages 216-224
A Lower Confidence Limit for the Multiple Correlation Coefficient....Pages 225-229
Analysis in Classes of Discontinuous Functions and Partial Differential Equations....Pages 230-248
The Behaviour of Solutions of Ordinary Differential Equations in Infinite Domains....Pages 249-257
Back Matter....Pages 258-261
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