This book contains two fundamental papers. The first is, in essence, a short monograph devoted to the theory of periodic motions in singularly perturbed systems. The second deals with structural properties of the solutions of a system having infinitely many switchings on a finite time interval to Hamiltonian systems with discontinuous right-hand side.

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.

This volume, dedicated to Carl Pearcy on the occasion of his 60th birthday, presents recent results in operator theory, nonselfadjoint operator algebras, measure theory and the theory of moments. The articles on these subjects have been contributed by leading area experts, many of whom were associated with Carl Pearcy as students or collaborators. The book testifies to his multifaceted interests and includes a biographical sketch and a list of publications.

The present book is the second 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 conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators 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 Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.

These essays broaden the debate on the nature of time. They provide an outline to the debate, presenting rival theories which demonstrate that such questions are intimately connected with issues in other fields of philosophy.