Modern Analysis 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 ofthebirthofMarkKrein, oneofthegreatestmathematiciansofthe20thcentury, was held in Odessa, Ukraine, on April 9-14, 2007. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to the theory of di? erential operators and mechanics. It opens with the description of the conference and a number of survey papers about the work of M. G. Krein. The main part of the book consists of original research papers presenting the state of the art in the area of di? erential operators. The ? rst volume of these proceedings, entitled Operator Theory and Related Topics, concerns other aspects of the conference. The two volumes will be of - terest to a wide-rangeof readership in pure and applied mathematics, physics and engineering sciences. OperatorTheory: AdvancesandApplications, Vol. 191, xi-xv c 2009Birkh auserVerlagBasel/Switzerland The World Dimension of the Heritage of a Ukrainian Mathematician International Conference "Modern Analysis and Applications" (MAA - 2007) (April 9-14, 2007, Odessa) Yu. BerezanskyandV. Gorbachuk This forum has been dedicated to the centennial birthday anniversary of one of the most prominent mathematicians of the twentieth century Mark Gr- orievich Krein, a corresponding member of the Academy of Sciences of the Ukr. SSR (1907-1989).

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