Harm Bart Bücher

Mathematicians operate within a rich tradition, engaging with colleagues through papers, books, and conferences worldwide. This collaborative environment fosters the validation of scientific results, transcending ethnic, political, or religious boundaries. Within this framework, certain individuals emerge as leaders, guiding their peers through complex challenges and leaving a lasting impact on the field. Such leadership requires a unique blend of broad knowledge, intuition, and charisma that unites people. Israel Gohberg, to whom this book is dedicated on his 80th birthday, exemplifies these exceptional qualities. His influence is evident in the contributions from those who worked alongside him or were touched by his work. The book features articles authored by Gohberg, some in collaboration with others, showcasing both mathematical insights and personal anecdotes. It includes tributes from colleagues, reflections on the life of a deceased friend, and highlights of Gohberg's work and character through speeches and reviews. Additionally, responses to the honors he received further illuminate the profound impact he has had on the mathematical community and beyond.

The present book deals with canonical factorization problems for di? erent classes of matrix and operator functions. Such problems appear in various areas of ma- ematics and its applications. The functions we consider havein common that they appear in the state space form or can be represented in such a form. The main results are all expressed in terms of the matrices or operators appearing in the state space representation. This includes necessary and su? cient conditions for canonical factorizations to exist and explicit formulas for the corresponding f- tors. Also, in the applications the entries in the state space representation play a crucial role. Thetheorydevelopedinthebookisbasedonageometricapproachwhichhas its origins in di? erent ? elds. One of the initial steps can be found in mathematical systems theory and electrical network theory, where a cascade decomposition of an input-output system or a network is related to a factorization of the associated transfer function. Canonical factorization has a long and interesting history which starts in the theory of convolution equations. Solving Wiener-Hopf integral equations is closely related to canonical factorization. The problem of canonical factorization also appears in other branches of applied analysis and in mathematical systems theory, in H -control theory in particular.

This book delineates the various types of factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, and the theory of job scheduling in operations research. The book presents a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions.

On November 12-14, 1997, a workshop was held at the Vrije Universiteit Amsterdam to celebrate M. A. Kaashoek's sixtieth birthday. The proceedings of this event are compiled in the present volume, which features contributions from 44 participants from various countries, including Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, the Netherlands, South Africa, Switzerland, Ukraine, and the USA. The workshop fostered a warm and friendly atmosphere, highlighted by 21 plenary lectures followed by engaging discussions. Support for the workshop came from several institutions, including the Vakgroep Wiskunde and the department of Mathematics and Computer Science at the Vrije Universiteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics at Erasmus University Rotterdam. The organizers express their gratitude for this support, which contributed significantly to the workshop's success. The volume includes a preface, a photograph of M. A. Kaashoek, his curriculum vitae, a list of his publications, and various addresses and reminiscences from participants, alongside detailed discussions on spectral components of selfadjoint operator matrices.