The conference is now over and enough time has passed for us to realize that the concensus of opinion of the participants is that it was indeed a successful and fruitful conference. This conference showed just how wide spread are the ideas of Otto Toeplitz, and how strong an influence his work has. The majority of participants contributed papers for this volume, which will help to bring to this interesting conference a wider audience. About the background and organization of the conference, the reader can learn from the opening address, which is included in place of an introduction. In my opinion this volume would be of interest to a wide public; experts in pure and applied mathematics as well as persons interested in the history of mathematics. The papers are divided into two sections. The first section is given to research papers, and the second to memorial papers. We are indebted to Professor G. K8the who allowed us to publish in the section of memorial papers the translation into English of his talk, given at a Colloquium in honour of Otto Toeplitz in Bonn. During the preparation of this volume great assistance was extended to us by Dr. Uri Toeplitz and Mrs. G. Riesel to whom I would like to express my sincere gratitude. I would like to take this opportunity to thank all persons and organizations who helped to make this conference such a success, and also Birkhauser Verlag for publishing this volume of the Proceedings.

Toeplitz Centennial: Toeplitz Memorial Conference in Operator Theory, Dedicated to the 100th Anniversary of the Birth of Otto Toeplitz, Tel Aviv, May ... Advances and Applications) (German Edition)

Science & Math

GOHBERG

Mathematics

Birkhauser

<p>This volume contains the proceedings of the Workshop on app1ications of linear operator theory to systems and networks, which was held at the Weizmann Institute of Science in the third week of June, 19S3,just be fore the MTNS Conference in Beersheva. For a 10ng time these subjects were studied indepen dent1y by mathematica1 ana1ysts and e1ectrica1 engineers. Never the1ess, in spite of the lack of communication, these two groups often deve10ped parallel theories, though in different languages, at different levels of genera1ity and typica11y quite different motivations. In the last severa1 years each side has become aware of the work of the other and there is a seeming1y ever increasing invo1vement of the abstract theories of factorization, extension and interpolation of operators (and operator/matrix va1ued functions) to the design and analysis of systems and net works. Moreover, the problems encountered in e1ectrica1 engineering have genera ted new mathematica1 problems, new approaches, and usefu1 new formu1ations. The papers contained in this volume constitute a more than representative se1ection of the presented talks and dis cussion at the workshop, and hopefu11y will also serve to give a reasonably accurate picture of the problems which are under active study today and the techniques which are used to deal with them.</p>

Topics in Operator Theory Systems and Networks: Workshop on Applications of Linear Operator Theory to Systems and Networks, Rehovot (Israel), June ... (Operator Theory: Advances and Applications)

Physics

I. Schur Methods in Operator Theory and Signal Processing (Operator Theory: Advances and Applications) (German Edition)

<p>The main part of this paper concerns Toeplitz operators of which the symbol W is an m x m matrix function defined on a disconnected curve r. The curve r is assumed to be the union of s + 1 nonintersecting simple smooth closed contours rOo r *. . . * rs which form the positively l oriented boundary of a finitely connected bounded domain in t. Our main requirement on the symbol W is that on each contour rj the function W is the restriction of a rational matrix function Wj which does not have poles and zeros on rj and at infinity. Using the realization theorem from system theory (see. e. g . * [1]. Chapter 2) the rational matrix function Wj (which differs from contour to contour) may be written in the form 1 (0. 1) W . (A) = I + C. (A - A. f B. A E r· J J J J J where Aj is a square matrix of size nj x n* say. B and C are j j j matrices of sizes n. x m and m x n . * respectively. and the matrices A. J x J J and Aj = Aj - BjC have no eigenvalues on r . (In (0. 1) the functions j j Wj are normalized to I at infinity.</p>

Constructive Methods of Wiener-Hopf Factorization (Operator Theory: Advances and Applications)

KAASHOEK

Format Paperback Subject Mathematics General Publisher Birkhauser

Minimal Factorization of Matrix and Operator Functions (Operator Theory: Advances and Applications)

BART