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2 Volume Set: Volume 1: ISBN 3-7643-6287-1 Volume 2: ISBN 3-7643-6288-X The two volumes (OT 117 and OT 118) consist of carefully edited and selected articles focussing on the main ideas, results, and methods of M.G. Krein. They contain some bibliographical material of M.G. Krein and a number of survey articles about his work. The main part of both volumes contains original research papers presenting the state of the art in operator theory and its applications. Description of 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 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. Series: Operator Theory: Advances and Applications, Vol. 117 Description of Volume II: 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 August 18-22, 1997. The conference focused on the main ideas, methods, results, and achievements of M.G. K