This book is dedicated to the memory of Israel Gohberg (1928-2009) - one of the great mathematicians of our time - who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg's mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

((keine o-Punkte, sondern 2 accents aigus auf dem o in Szokefalvi, s. auch Titel ))

In August 1999, an international conference was held in Szeged, Hungary, in honor of Bela Szokefalvi-Nagy, one of the founders and main contributors of modern operator theory. This volume contains some of the papers presented at the meeting, complemented by several papers of experts who were unable to attend. These 35 refereed articles report on recent and original results in various areas of operator theory and connected fields, many of them strongly related to contributions of Sz.-Nagy. The scientific part of the book is preceeded by fifty pages of biographical material, including several photos."

In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are dedicated to different problems in matrix and operator theory, especially to the areas in which Peter contributed so richly. At our request, Peter agreed to write an autobiographical paper, which appears at the beginning of the volume. It continues with the list of Peter's publications. We believe that this volume will pay tribute to Peter on his outstanding achievements in different areas of mathematics. 1. Gohberg, H. Langer P ter Lancast r *1929 Operator Theory: Advances and Applications, Vol. 130, 1- 7 (c) 2001 Birkhiiuser Verlag Basel/Switzerland My Life and Mathematics Peter Lancaster I was born in Appleby, a small county town in the north of England, on November 14th, 1929. I had two older brothers and was to have one younger sister. My family moved around the north of England as my father's work in an insurance company required."

This book is dedicated to the memory of Israel Gohberg (1928-2009) - one of the great mathematicians of our time - who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg's mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

This is the ?rst of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary ofthebirthofMarkKrein,oneofthegreatestmathematiciansofthe20thcentury, was held in Odessa, Ukraine, on April 9-14, 2007. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This?rstvolumeisdevotedtotheoperatortheoryandrelatedtopics. Itopens withthebiographypapersaboutM. G. Kreinandanumberofsurveypapersabout his work. The mainpartof the book consistsof originalresearchpaperspresenting the state of the art in operator theory and its application. The second volume of these proceedings, entitled Di?erential Operators and Mechanics, concerns 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. The editors are sincerely grateful to the persons who contributed to the preparation of these proceedings: Sergei Marchenko, Myroslav Sushko, Kostyantyn Yusenko and Vladimir Zavalnyuk. Mark Grigorievich Krein, 1907-1989 Operator Theory: Advances and Applications, Vol. 190, xi-xx c 2009 Birkh. auser Verlag Basel/Switzerland Mark Grigorievich Krein (on his 100th birthday anniversary) V. M. Adamyan, D. Z. Arov, Yu. M. Berezansky, V. I. Gorbachuk, M. L. Gorbachuk, V. A. Mikhailets and A. M. Samoilenko April 3, 2007, is the l00th anniversary of the birth of Mark Grigorievich Krein, one of the most celebrated mathematicians of the 20th century, whose whole life was closely connected with Ukraine.

This is the second of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary ofthebirthofMarkKrein,oneofthegreatestmathematiciansofthe20thcentury, was held in Odessa, Ukraine, on April 9-14, 2007. The conference focused on the main ideas, methods, results, and achievements of M.G. Krein. This second volume is devoted to the theory of di?erential operators and mechanics. It opens with the description of the conference 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 di?erential operators. The ?rst volume of these proceedings, entitled Operator Theory and Related Topics, concerns other aspects of the conference. The two volumes will be of - terest to a wide-rangeof readership in pure and applied mathematics, physics and engineering sciences. OperatorTheory: AdvancesandApplications,Vol.191, xi-xv c 2009Birkh. auserVerlagBasel/Switzerland The World Dimension of the Heritage of a Ukrainian Mathematician International Conference "Modern Analysis and Applications" (MAA - 2007) (April 9-14, 2007, Odessa) Yu. BerezanskyandV.Gorbachuk This forum has been dedicated to the centennial birthday anniversary of one of the most prominent mathematicians of the twentieth century Mark Gr- orievich Krein, a corresponding member of the Academy of Sciences of the Ukr. SSR (1907-1989).

This volume contains papers written by participants of the 6th Workshop on - erator Theory in Krein Spaces and Operator Polynomials, which was held at the Technische Universit. at Berlin, Germany, December 14 to 17, 2006. This workshop was attended by 67 participants from 14 countries. The lectures covered topics from spectral and perturbation theory of linear operators in inner product spaces and from operator polynomials. They included the theory of generalized Nevanlinna and Schur functions, di?erential operators, singular perturbations, de Branges spaces, scattering problems, block numerical ranges, nonnegative matrices and relations. All these topics are re?ected in the present volume. Besides, it contains an after dinner speech from an earlier wo- shop, which we think may be of interest for the reader, as well as a speech on the occasion of the retirement of Peter Jonas. It is a pleasure to acknowledge the substantial ?nancial support received from the - Deutsche Forschungsgemeinschaft (DFG), - Berlin Mathematical School (BMS), - DFG-Forschungszentrum MATHEON "Mathematik fur .. Schlussel- .. technologien", - Institute of Mathematics of the Technische Universit. at Berlin. WewouldalsoliketothankPetraGrimbergerforhergreathelpintheorganisation. Without her assistance the workshop might not have taken place.

This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation, and extension theory of linear operators and relations in inner product spaces.

rd This volume contains papers written by the participants of the 3 Workshop on Operator Theory in Krein spaces and Nonlinear Eigenvalue Problems, held at the Technische Universit. at Berlin, Germany, December 12 to 14, 2003. The workshop covered topics from spectral, perturbation and extension t- ory of linear operators in Krein spaces. They included generalized Nevanlinna functions and related classes of functions, boundary value problems for di?erential operators, spectral problems for matrix polynomials, and perturbation problems forsecondorderevolutionequations.Alltheseproblemsarere?ectedinthepresent volume. The workshop was attended by 46 participants from 12 countries. It is a pleasure to acknowledge the substantial ?nancial support received from the - Research Training Network HPRN-CT-2000-00116 "Analysis and Operators" by the European Community, - DFG-Forschungszentrum MATHEON "Mathematik fur .. Schlussel- .. technologien", - Institute of Mathematics of the Technische Universit. at Berlin. We would also like to thank Petra Grimberger for her great help. Last but not least, special thanks are due to Jussi Behrndt, Christian Mehl and Carsten Trunk for their excellent workin the organisationof the workshopand the preparationof this volume. Without their assistance the workshop might not have taken place. The Editors Operator Theory: Advances and Applications, Vol. 162, 1-17 c 2005 Birkh. auser Verlag Basel/Switzerland Partial Non-stationary Perturbation Determinants for a Class of J-symmetric Operators Vadim Adamyan, Peter Jonas and Heinz Langer Abstract. We consider the partial non-stationary perturbation determinant (1) itA ?itH ? (t):=det e P e ,t? R.

((keine o-Punkte, sondern 2 accents aigus auf dem o in Szokefalvi, s. auch Titel ))

In August 1999, an international conference was held in Szeged, Hungary, in honor of Bela Szokefalvi-Nagy, one of the founders and main contributors of modern operator theory. This volume contains some of the papers presented at the meeting, complemented by several papers of experts who were unable to attend. These 35 refereed articles report on recent and original results in various areas of operator theory and connected fields, many of them strongly related to contributions of Sz.-Nagy. The scientific part of the book is preceeded by fifty pages of biographical material, including several photos."

The book is complemented by biographical information. This volume is dedicated to Peter Lancaster, an outstanding expert in operator and matrix theory, numerical analysis and applications, on the occasion of his seventieth birthday. The book contains a selection of recent original research papers in linear algebra and analysis, areas in which Peter Lancaster was very active. The articles are complemented by biographical data and a list of publications. Contributed volume in honor of Peter Lancaster, an outstanding expert in operator theory, matrix theory and numerical analysis. The articles have been carefully selected and refereed and cover topics in linear algebra and analysis where Peter Lancaster was very active.

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.