Topics in Differential and Integral Equations and Operator Theory

1. Front Matter

   Pages I-IX

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2. The Basic Propositions of the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients

   • M. G. Krein

   Pages 1-105

3. On Certain New Studies in the Perturbation Theory for Selfadjoint Operators

   • M. G. Krein

   Pages 107-172

4. On Nonlinear Integral Equations which Play a Role in the Theory of Wiener-Hopf Equations. I, II

   • M. G. Krein

   Pages 173-242

5. On a Pair Integral Equation and its Transpose

   • I. C. Gohberg, M. G. Krein

   Pages 243-274

6. New Inequalities for the Characteristic Numbers of Integral Equations with Smooth Kernels

   • I. C. Gohberg, M. G. Krein

   Pages 275-293

7. A Contribution to the Theory of S-Matrices of Canonical Differential Equations with Summable Potential

   • M. G. Krein, F. E. Melik-Adamyan

   Pages 295-302

In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were written more than twenty years ago, the passage of time has not decreased their value. They are as fresh and vital as if they had been written only yesterday. These papers contain a wealth of ideas, and will serve as a source of stimulation and inspiration for experts and beginners alike. The first paper is dedicated to the theory of canonical linear differential equations, with periodic coefficients. It focuses on the study of linear Hamiltonian systems with bounded solutions which stay bounded under small perturbations of the system. The paper uses methods from operator theory in finite and infinite dimensional spaces and complex analysis. For an account of more recent literature which was generated by this paper see AMS Translations (2), Volume 93, 1970, pages 103-176 and Integral Equations and Operator Theory, Volume 5, Number 5, 1982, pages 718-757.

• Integral
• Integral equation
• perturbation
• perturbation theory

• School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel

  I. Gohberg

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