Ebook: Modern Analysis and Applications: The Mark Krein Centenary Conference Volume 2: Differential Operators and Mechanics

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.

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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.

Content:
Front Matter....Pages i-ix
The World Dimension of the Heritage of a Ukrainian Mathematician....Pages xi-xv
Front Matter....Pages 1-1
Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth....Pages 3-17
Krein Systems....Pages 19-36
Spectral Theory of the Infinite Block Jacobi Type Normal Matrices, Orthogonal Polynomials on a Complex Domain, and the Complex Moment Problem....Pages 37-50
On Geometrical and Analytical Aspects in Formulations of Problems of Classic and Non-classic Continuum Mechanics....Pages 51-79
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr?dinger Operators on Bounded Lipschitz Domains....Pages 81-113
On Behavior of Weak Solutions of Operator Differential Equations on (0, ?)....Pages 115-126
Some Modern Methods in Mechanics of Cracks....Pages 127-142
A Method of the Green’s Functions for Quasistatic Thermoelasticity Problems in Layered Thermosensitive Bodies under Complex Heat Exchange....Pages 143-154
On the Application of the M.G. Krein Method for the Solution of Integral Equations in Contact Problems in Elasticity Theory....Pages 155-171
The Stress Concentration in the Neighborhood of the Spherical Crack Inside the Infinite Elastic Cone....Pages 173-186
Pseudospectral Functions for Canonical Differential Systems....Pages 187-219
On Wave Hyperbolic Model for Disturbance Propagation in Magnetic Fluid....Pages 221-225
Front Matter....Pages 227-227
High-accuracy Stable Difference Schemes for Well-posed NBVP....Pages 229-252
The Factorization of the Flow, Defined by the Euler-Poisson’s Equations....Pages 253-271
On a Moment Problem on a Curve Connected with Ill-posed Boundary Value Problems for a PDE and Some Other Problems....Pages 273-289
The Construction and Analysis of a Posteriori Error Estimators for Piezoelectricity Stationary Problems....Pages 291-304
Remarks about Observables for the Quantum Mechanical Harmonic Oscillator....Pages 305-321
Remark on Spectral Rigidity for Magnetic Schr?dinger Operators....Pages 323-329
On Holomorphic Solutions of Some Implicit Linear Differential Equations in a Banach Space....Pages 331-340
Front Matter....Pages 227-227
Groups of Operators for Evolution Equations of Quantum Many-particle Systems....Pages 341-355
Box-like Shells with Longitudinal Cracks....Pages 357-364
Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces of Two Anticommuting Variables....Pages 365-379
On the Modified Spectral Stefan Problem and Its Abstract Generalizations....Pages 381-394
The Discontinuous Solution for the Piece-homogeneous Transversal Isotropic Medium....Pages 395-406
On the Carleman Ultradifferentiability of Weak Solutions of an Abstract Evolution Equation....Pages 407-443
On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy....Pages 445-454
Elliptic Problems and H?rmander Spaces....Pages 455-478
Connection of Solutions of Abstract Paired Equations in Rings with Factorization Pairs....Pages 479-484
The Dynamic Problems About the Definition of Stress State Near Thin Elastic Inclusions Under the Conditions of Perfect Coupling....Pages 485-498
Fourier Multipliers and Comparison of Linear Operators....Pages 499-513
Forced Vibrations of the Infinite Shell of the Square Cross Section....Pages 515-520

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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.

Content:
Front Matter....Pages i-ix
The World Dimension of the Heritage of a Ukrainian Mathematician....Pages xi-xv
Front Matter....Pages 1-1
Bilateral Asymptotic Solution of One Class of Dual Integral Equations of the Static Contact Problems for the Foundations Inhomogeneous in Depth....Pages 3-17
Krein Systems....Pages 19-36
Spectral Theory of the Infinite Block Jacobi Type Normal Matrices, Orthogonal Polynomials on a Complex Domain, and the Complex Moment Problem....Pages 37-50
On Geometrical and Analytical Aspects in Formulations of Problems of Classic and Non-classic Continuum Mechanics....Pages 51-79
Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr?dinger Operators on Bounded Lipschitz Domains....Pages 81-113
On Behavior of Weak Solutions of Operator Differential Equations on (0, ?)....Pages 115-126
Some Modern Methods in Mechanics of Cracks....Pages 127-142
A Method of the Green’s Functions for Quasistatic Thermoelasticity Problems in Layered Thermosensitive Bodies under Complex Heat Exchange....Pages 143-154
On the Application of the M.G. Krein Method for the Solution of Integral Equations in Contact Problems in Elasticity Theory....Pages 155-171
The Stress Concentration in the Neighborhood of the Spherical Crack Inside the Infinite Elastic Cone....Pages 173-186
Pseudospectral Functions for Canonical Differential Systems....Pages 187-219
On Wave Hyperbolic Model for Disturbance Propagation in Magnetic Fluid....Pages 221-225
Front Matter....Pages 227-227
High-accuracy Stable Difference Schemes for Well-posed NBVP....Pages 229-252
The Factorization of the Flow, Defined by the Euler-Poisson’s Equations....Pages 253-271
On a Moment Problem on a Curve Connected with Ill-posed Boundary Value Problems for a PDE and Some Other Problems....Pages 273-289
The Construction and Analysis of a Posteriori Error Estimators for Piezoelectricity Stationary Problems....Pages 291-304
Remarks about Observables for the Quantum Mechanical Harmonic Oscillator....Pages 305-321
Remark on Spectral Rigidity for Magnetic Schr?dinger Operators....Pages 323-329
On Holomorphic Solutions of Some Implicit Linear Differential Equations in a Banach Space....Pages 331-340
Front Matter....Pages 227-227
Groups of Operators for Evolution Equations of Quantum Many-particle Systems....Pages 341-355
Box-like Shells with Longitudinal Cracks....Pages 357-364
Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces of Two Anticommuting Variables....Pages 365-379
On the Modified Spectral Stefan Problem and Its Abstract Generalizations....Pages 381-394
The Discontinuous Solution for the Piece-homogeneous Transversal Isotropic Medium....Pages 395-406
On the Carleman Ultradifferentiability of Weak Solutions of an Abstract Evolution Equation....Pages 407-443
On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy....Pages 445-454
Elliptic Problems and H?rmander Spaces....Pages 455-478
Connection of Solutions of Abstract Paired Equations in Rings with Factorization Pairs....Pages 479-484
The Dynamic Problems About the Definition of Stress State Near Thin Elastic Inclusions Under the Conditions of Perfect Coupling....Pages 485-498
Fourier Multipliers and Comparison of Linear Operators....Pages 499-513
Forced Vibrations of the Infinite Shell of the Square Cross Section....Pages 515-520
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