Modern Analysis and Applications (eBook)

Contents 6
Preface 9
The World Dimension of the Heritage of a Ukrainian Mathematician 10
Part 1 Plenary Talks 15
Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth 16
Krein Systems 31
Spectral Theory of the Infinite Block Jacobi Type Normal Matrices, Orthogonal Polynomials on a Complex Domain, and the Complex Moment Problem 49
On Geometrical and Analytical Aspects in Formulations of Problems of Classic and Non- classic Continuum Mechanics 63
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains 92
On Behavior of Weak Solutions of Operator Differential Equations on (0,8) 125
Some Modern Methods in Mechanics of Cracks 137
A Method of the Green’s Functions for Quasistatic Thermoelasticity Problems in Layered Thermosensitive Bodies under Complex Heat Exchange 153
On the Application of the M.G. Krein Method for the Solution of Integral Equations in Contact Problems in Elasticity Theory 165
The Stress Concentration in the Neighborhood of the Spherical Crack Inside the Infinite Elastic Cone 182
Pseudospectral Functions for Canonical Differential Systems 196
On Wave Hyperbolic Model for Disturbance Propagation in Magnetic Fluid 229
Part 2 Research Papers 234
High-accuracy Stable Difference Schemes for Well- posed NBVP 235
The Factorization of the Flow, Defined by the Euler- Poisson’s Equations 259
On a Moment Problem on a Curve Connected with Ill- posed Boundary Value Problems for a PDE and Some Other Problems 278
The Construction and Analysis of a Posteriori Error Estimators for Piezoelectricity Stationary Problems 295
Remarks about Observables for the Quantum Mechanical Harmonic Oscillator 309
Remark on Spectral Rigidity for Magnetic Schrödinger Operators 326
On Holomorphic Solutions of Some Implicit Linear Differential Equations in a Banach Space 333
Groups of Operators for Evolution Equations of Quantum Many- particle Systems 343
Box-like Shells with Longitudinal Cracks 358
Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces of Two Anticommuting Variables 366
On the Modified Spectral Stefan Problem and Its Abstract Generalizations 381
The Discontinuous Solution for the Piece- homogeneous Transversal Isotropic Medium 395
On the Carleman Ultradifferentiability of Weak Solutions of an Abstract Evolution Equation 407
On the Equivalence of Different Lax Pairs for the Kac– van Moerbeke Hierarchy 444
Elliptic Problems and Hörmander Spaces 454
Connection of Solutions of Abstract Paired Equations in Rings with Factorization Pairs 478
The Dynamic Problems About the Definition of Stress State Near Thin Elastic Inclusions Under the Conditions of Perfect Coupling 484
Fourier Multipliers and Comparison of Linear Operators 498
Forced Vibrations of the Infinite Shell of the Square Cross Section 513