Modern Analysis and Applications: The Mark Krein Centenary Conference - Volume 2: Differential Operators and Mechanics (Operator Theory: Advances and Applications)

This is the second of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary of the birth of Mark Krein, one of the greatest mathematicians of the 20th century, was held in Odessa, Ukraine, on April 9-14, 2007. The papers describe the contemporary development of subjects influenced by Krein, such as the theory of operators in Hilbert and Krein spaces, differential operators, applications of functional analysis in function theory, theory of networks and systems, mathematical physics and mechanics. Contents......Page 6 Preface......Page 10 The World Dimension of the Heritage of a Ukrainian Mathematician......Page 12 Part 1: Plenary Talks......Page 17 Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth......Page 19 Krein Systems......Page 35 Spectral Theory of the Infinite Block Jacobi Type Normal Matrices, Orthogonal Polynomials on a Complex Domain, and the Complex Moment Problem......Page 53 On Geometrical and Analytical Aspects in Formulations of Problems of Classic and Non-classic Continuum Mechanics......Page 67 Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains......Page 97 On Behavior of Weak Solutions of Operator Differential Equations on (0,∞)......Page 131 Some Modern Methods in Mechanics of Cracks......Page 143 A Method of the Green's Functions for Quasistatic Thermoelasticity Problems in Layered Thermosensitive Bodies under Complex Heat Exchange......Page 159 On the Application of the M.G. Krein Method for the Solution of Integral Equations in Contact Problems in Elasticity Theory......Page 171 The Stress Concentration in the Neighborhood of the Spherical Crack Inside the Infinite Elastic Cone......Page 189 Pseudospectral Functions for Canonical Differential Systems......Page 203 On Wave Hyperbolic Model for Disturbance Propagation in Magnetic Fluid......Page 237 Part 2: Research Papers......Page 243 High-accuracy Stable Difference Schemes for Well-posed NBVP......Page 245 The Factorization of the Flow, Defined by the Euler-Poisson's Equations......Page 269 On a Moment Problem on a Curve Connected with Ill-posed Boundary Value Problems for a PDE and Some Other Problems......Page 289 The Construction and Analysis of a Posteriori Error Estimators for Piezoelectricity Stationary Problems......Page 307 Remarks about Observables for the Quantum Mechanical Harmonic Oscillator......Page 321 Remark on Spectral Rigidity for Magnetic Schrödinger Operators......Page 339 On Holomorphic Solutions of Some Implicit Linear Differential Equations in a Banach Space......Page 347 Groups of Operators for Evolution Equations of Quantum Many-particle Systems......Page 357 Box-like Shells with Longitudinal Cracks......Page 373 Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces of Two Anticommuting Variables......Page 381 On the Modified Spectral Stefan Problem and Its Abstract Generalizations......Page 397 The Discontinuous Solution for the Piece-homogeneous Transversal Isotropic Medium......Page 411 On the Carleman Ultradifferentiability of Weak Solutions of an Abstract Evolution Equation......Page 423 On the Equivalence of Different Lax Pairs for the Kac–van Moerbeke Hierarchy......Page 461 Elliptic Problems and Hörmander Spaces......Page 471 Connection of Solutions of Abstract Paired Equations in Rings with Factorization Pairs......Page 495 The Dynamic Problems About the Definition of Stress State Near Thin Elastic Inclusions Under the Conditions of Perfect Coupling......Page 501 Fourier Multipliers and Comparison of Linear Operators......Page 515 Forced Vibrations of the Infinite Shell of the Square Cross Section......Page 531