Ebook: Differential Operators and Related Topics: Proceedings of the Mark Krein International Conference on Operator Theory and Applications, Odessa, Ukraine, August 18–22, 1997 Volume I

The present book is the first of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The confer­ encefocused onthemain ideas, methods, results, andachievementsofM.G. Krein. This first volume is devoted to the theory of differential operators and related topics. It opens with a description of the conference, biographical material and a number of survey papers about the work of M.G. Krein. The main part of the book consists oforiginal research papers presenting the stateofthe art in the area ofdifferential operators. The second volume of these proceedings, entitled Operator Theory and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface............................................................. v Table of Contents VII Picture of M.G. Krein Xl About the Mark Krein International Conference . Mark Grigorevich Krein (A short biography) 5 I. Gohberg The Seminar on Ship Hydrodynamics, Organized by M.G. Krein 9 v.G. Sizov Review Papers: The Works ofM.G. Krein on Eigenfunction Expansion for Selfadjoint Operators and their Applications and Development 21 Yu.M. Berezansky M.G. Krein and the Extension Theory of Symmetric Operators.

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The present book is the first of the two volume proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine, from August 18-22, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This first volume is devoted to the theory of differential operators and related topics. It opens with a description of the conference, biographical material 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 differential operators. The second volume of these proceedings, entitled Operator Theory and Related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide range of readership in pure and applied mathematics, physics and engineering sciences.

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The present book is the first of the two volume proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine, from August 18-22, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This first volume is devoted to the theory of differential operators and related topics. It opens with a description of the conference, biographical material 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 differential operators. The second volume of these proceedings, entitled Operator Theory and Related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide range of readership in pure and applied mathematics, physics and engineering sciences.
Content:
Front Matter....Pages i-xi
About the Mark Krein International Conference....Pages 1-4
Mark Grigorevich Krein (A Short Biography)....Pages 5-8
The Seminar on Ship Hydrodynamics, Organized by Professor M.G. Krein....Pages 9-20
The Works of M.G. Krein on Eigenfunction Expansion for Selfadjoint Operators and their Applications and Development....Pages 21-43
M.G. Krein and Extension Theory of Symmetric Operators. Theory of Entire Operators....Pages 45-58
Works by M.G. Krein on Inverse Problems....Pages 59-69
The Spectrum of Periodic Point Perturbations and the Krein Resolvent Formula....Pages 71-86
The Periodic Choquard Equation....Pages 87-99
On the Best Constant in a Poincare-Sobolev Inequality....Pages 101-109
On Solutions of Parabolic Equations from Families of Banach Spaces Dependent on Time....Pages 111-125
Canonical Systems on the Line with Rational Spectral Densities: Explicit Formulas....Pages 127-139
Oscillations in Systems with Periodic Coefficients and Sector-restricted Nonlinearities....Pages 141-154
Differential Operator Matrices of Mixed Order with Periodic Coefficients....Pages 155-164
Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging....Pages 165-186
Functional Means, Convolution Operators and Semigroups....Pages 187-198
The Inverse Spectral Problem for First Order Systems on the Half Line....Pages 199-238
Exact Solution of the Marchenko Equation Relevant to Inverse Scattering on the Line....Pages 239-259
An Arbitrary Oriented Crack in the Box Shell....Pages 261-266
Homogeneity of a String having Three Unperturbed Spectra....Pages 267-271
On the Integro-differential Equation of a Torsion of an Elastic Medium Including a Cylindrical Crack....Pages 273-280
Green’s Formula and Theorems on Isomorphisms for General Elliptic Problems for Douglis-Nirenberg Elliptic Systems....Pages 281-299
Sobolev’s Problem in Complete Scale of Banach Spaces....Pages 301-312
On Simple Waves with Profiles in the form of some Special Functions-Chebyshov-Hermite, Mathieu, Whittaker-in Two-phase Media....Pages 313-322
Inverse Spectral Problem Related to the N-wave Equation....Pages 323-338
Degenerated Hyperbolic Approximations of the Wave Theory of Elastic Plates....Pages 339-353
Elliptic Problems with a Shift in Complete Scales of Sobolev-Type Spaces....Pages 355-358
On the Extremal Regularization of the Variational Inequalities with Multivalued Operators....Pages 359-370
Poly-Fock Spaces....Pages 371-386
The Diffraction of Elastic Shear Wave on the Circular Cylinder which is Situated in the Elastic Halfspace....Pages 387-392
On M.G. Krein’s Spectral Shift Function for Canonical Systems of Differential Equations....Pages 393-417
Back Matter....Pages 419-420

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The present book is the first of the two volume proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine, from August 18-22, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This first volume is devoted to the theory of differential operators and related topics. It opens with a description of the conference, biographical material 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 differential operators. The second volume of these proceedings, entitled Operator Theory and Related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide range of readership in pure and applied mathematics, physics and engineering sciences.
Content:
Front Matter....Pages i-xi
About the Mark Krein International Conference....Pages 1-4
Mark Grigorevich Krein (A Short Biography)....Pages 5-8
The Seminar on Ship Hydrodynamics, Organized by Professor M.G. Krein....Pages 9-20
The Works of M.G. Krein on Eigenfunction Expansion for Selfadjoint Operators and their Applications and Development....Pages 21-43
M.G. Krein and Extension Theory of Symmetric Operators. Theory of Entire Operators....Pages 45-58
Works by M.G. Krein on Inverse Problems....Pages 59-69
The Spectrum of Periodic Point Perturbations and the Krein Resolvent Formula....Pages 71-86
The Periodic Choquard Equation....Pages 87-99
On the Best Constant in a Poincare-Sobolev Inequality....Pages 101-109
On Solutions of Parabolic Equations from Families of Banach Spaces Dependent on Time....Pages 111-125
Canonical Systems on the Line with Rational Spectral Densities: Explicit Formulas....Pages 127-139
Oscillations in Systems with Periodic Coefficients and Sector-restricted Nonlinearities....Pages 141-154
Differential Operator Matrices of Mixed Order with Periodic Coefficients....Pages 155-164
Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging....Pages 165-186
Functional Means, Convolution Operators and Semigroups....Pages 187-198
The Inverse Spectral Problem for First Order Systems on the Half Line....Pages 199-238
Exact Solution of the Marchenko Equation Relevant to Inverse Scattering on the Line....Pages 239-259
An Arbitrary Oriented Crack in the Box Shell....Pages 261-266
Homogeneity of a String having Three Unperturbed Spectra....Pages 267-271
On the Integro-differential Equation of a Torsion of an Elastic Medium Including a Cylindrical Crack....Pages 273-280
Green’s Formula and Theorems on Isomorphisms for General Elliptic Problems for Douglis-Nirenberg Elliptic Systems....Pages 281-299
Sobolev’s Problem in Complete Scale of Banach Spaces....Pages 301-312
On Simple Waves with Profiles in the form of some Special Functions-Chebyshov-Hermite, Mathieu, Whittaker-in Two-phase Media....Pages 313-322
Inverse Spectral Problem Related to the N-wave Equation....Pages 323-338
Degenerated Hyperbolic Approximations of the Wave Theory of Elastic Plates....Pages 339-353
Elliptic Problems with a Shift in Complete Scales of Sobolev-Type Spaces....Pages 355-358
On the Extremal Regularization of the Variational Inequalities with Multivalued Operators....Pages 359-370
Poly-Fock Spaces....Pages 371-386
The Diffraction of Elastic Shear Wave on the Circular Cylinder which is Situated in the Elastic Halfspace....Pages 387-392
On M.G. Krein’s Spectral Shift Function for Canonical Systems of Differential Equations....Pages 393-417
Back Matter....Pages 419-420
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