Differential Operators and Related Topics

1. Front Matter

   Pages i-xi

   PDF

2. About the Mark Krein International Conference

   • V. M. Adamyan, I. Gohberg, M. Gorbachuk, V. Gorbachuk, M. A. Kaashoek, H. Langer et al.

   Pages 1-4

3. Mark Grigorevich Krein (A Short Biography)

   • Israel Gohberg

   Pages 5-8

4. The Seminar on Ship Hydrodynamics, Organized by Professor M.G. Krein

   • V. G. Sizov

   Pages 9-20

5. The Works of M.G. Krein on Eigenfunction Expansion for Selfadjoint Operators and their Applications and Development

   • Yu. M. Berezansky

   Pages 21-43

6. M.G. Krein and Extension Theory of Symmetric Operators. Theory of Entire Operators

   • M. L. Gorbachuk, V. I. Gorbachuk

   Pages 45-58

7. Works by M.G. Krein on Inverse Problems

   • L. A. Sakhnovich

   Pages 59-69

8. The Spectrum of Periodic Point Perturbations and the Krein Resolvent Formula

   • J. Brüning, V. A. Geyler

   Pages 71-86

9. The Periodic Choquard Equation

   • Ya. M. Dymarskii

   Pages 87-99

10. On the Best Constant in a Poincare-Sobolev Inequality

    • Yuri V. Egorov

    Pages 101-109

11. On Solutions of Parabolic Equations from Families of Banach Spaces Dependent on Time

    • S. D. Eidelman, S. D. Ivasyshen

    Pages 111-125

12. Canonical Systems on the Line with Rational Spectral Densities: Explicit Formulas

    • I. Gohberg, M. A. Kaashoek, A. L. Sakhnovich

    Pages 127-139

13. Oscillations in Systems with Periodic Coefficients and Sector-restricted Nonlinearities

    • A. Halanay, V. L. Răsvan

    Pages 141-154

14. Differential Operator Matrices of Mixed Order with Periodic Coefficients

    • R. Hryniv, A. Shkalikov, A. Vladimirov

    Pages 155-164

15. Asymptotics of Generalized Eigenvectors for Unbounded Jacobi Matrices with Power-like Weights, Pauli Matrices Commutation Relations and Cesaro Averaging

    • Jan Janas, Serguei Naboko

    Pages 165-186

16. Functional Means, Convolution Operators and Semigroups

    • S. V. Koshkin

    Pages 187-198

17. The Inverse Spectral Problem for First Order Systems on the Half Line

    • Matthias Lesch, Mark M. Malamud

    Pages 199-238

18. Exact Solution of the Marchenko Equation Relevant to Inverse Scattering on the Line

    • Cornelis van der Mee

    Pages 239-259

19. An Arbitrary Oriented Crack in the Box Shell

    • V. I. Migdalski, V. V. Reut

    Pages 261-266

20. Homogeneity of a String having Three Unperturbed Spectra

    • Vyacheslav N. Pivovarchik

    Pages 267-271

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.

• Approximation
• applied mathematics
• banach spaces
• convolution
• differential equation
• differential operator
• eigenvector
• extrema
• homogenization
• operator
• operator theory
• perturbation
• perturbation theory
• special function
• wave equation

• Department of Theoretical Physics, University of Odessa, Odessa, Ukraine

  V. M. Adamyan

• Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

  I. Gohberg

• Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

  M. Gorbachuk, V. Gorbachuk

• Department of Mathematics, Vrije Universiteit, Amsterdam, The Netherlands

  M. A. Kaashoek

• Department of Mathematics, Technical University of Vienna, Vienna, Austria

  H. Langer

• Institute of Mathematics, Economics and Mechanics, Odessa State University, Odessa, Ukraine

  G. Popov

Policies and ethics