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This book is devoted to the theory of entire Hermitian operators, an important branch of functional analysis harmoniously combining the methods of operator theory and the theory of analytic functions. This theory anables various problems of classical and modern analysis to be looked at from a uniform point of view. In addition, it serves as a source for setting and solving many new problems in both theories. The three chapters of the book are based on the notes written by his students of M. G. Krein's lectures on the theory of entire operators with (1,1)- deficiency index which he delivered...

This text is devoted to the theory of entire operators, which was founded by M.G. Krein. The theory lies at the junction of the spectral theory of Hermitian operators and the theory of analytic functions, combining the methods of each. The purpose of this text is to show how problems of both classical and modern analysis can be looked at from the point of view of entire operator theory. This is one of the first systematic presentations of the basic concepts of Krein's theory and its applications, and its study of his unpublished lectures and his works gives recognition to the unique approach...

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...