The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering theory within the framework of operatortheory in Hilbert space. The term Mathematical Scattering theory deno...
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ISBN:
(数字)9783034854405
ISBN:
(纸本)9783034854429
The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering theory within the framework of operatortheory in Hilbert space. The term Mathematical Scattering theory denotes that theory which is on the one hand the common mathematical foundation of several physical scattering theories (scattering of quantum objects, of classical waves and particles) and on the other hand a branch of operatortheory devoted to the study of the behavior of the continuous part of perturbed operators (some authors also use the term Abstract Scattering theory). EBBential contributions to the development of this theory are due to K. FRIEDRICHS, J. CooK, T. KATo, J. M. JAuCH, S. T. KURODA, M.S. BmMAN, M.G. KREiN, L. D. FAD DEEV, R. LAVINE, W. 0. AMREIN, B. SIMoN, D. PEARSON, V. ENss, and others. It seems to the authors that the theory has now reached a sufficiently developed state that a self-contained presentation of the topic is justified.
This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russi...
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ISBN:
(数字)9783764389567
ISBN:
(纸本)9783764389550
This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russian. The papers were wr- ten more than thirty years ago, but time showed their importance and growing in?uence in pure and applied mathematics and engineering. The book is divided into two parts. The ?rst ?ve papers, written by I. Gohberg and G. Heinig, form the ?rst part. They are related to the inversion of ?nite block Toeplitz matrices and their continuous analogs (direct and inverse problems) and the theory of discrete and continuous resultants. The second part consists of eight papers by I. Gohberg and N. Krupnik. They are devoted to the theory of one dimensional singular integral operators with discontinuous co- cients on various spaces. Special attention is paid to localization theory, structure of the symbol, and equations with shifts. ThisbookgivesanEnglishspeakingreaderauniqueopportunitytogetfam- iarized with groundbreaking work on the theory of Toepliz matrices and singular integral operators which by now have become classical. In the process of the preparation of the book the translator and the editors took care of several misprints and unessential misstatements. The editors would like to thank the translator A. Karlovich for the thorough job he has done. Our work on this book was started when Israel Gohberg was still alive. We see this book as our tribute to a great mathematician.
The Eleventh International Transport theory Conference and Symposium in honor of the sixty-fifth birthday of Kenneth Case and the sixtieth birthday of Paul Zweifel was held in Blacksburg, Virginia, during May 22-26, 1...
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ISBN:
(数字)9783034856751
ISBN:
(纸本)9783034856775
The Eleventh International Transport theory Conference and Symposium in honor of the sixty-fifth birthday of Kenneth Case and the sixtieth birthday of Paul Zweifel was held in Blacksburg, Virginia, during May 22-26, 1989, on the campus of Virginia Polytechnic Institute and State University (Virginia Tech). This volume consists of a selection of the invited papers delivered at the Conference, and represents a cross section of the research currently being carried out in the field of transport theory. The volume is divided into two sections. The Symposium lectures are intended each to summarize an important aspect of transport theory, as well as to present timely new results of the author's research interest. The Conference lectures are contributions of each author on his current research. As has been the custom in this series of conferences, each lecturer was invited to participate by the organizing committee of the Conference: W. Greenberg, Virginia Tech, chairman; V. Boffi, Universita di Firenze; N. Corngold, California Institute of Technology; B. Ganapol, University of Arizona; N. McCormick, University of Washington; P. Nelson, Texas Tech; G. Pomraning, University of California, Los Angeles. The Eleventh International Transport theory Conference was funded by generous con tributions from Science applications International Corporation, R. Beyster, president, and from Virginia Polytechnic Institute and State University. Conference participants, and, we believe, researchers in this and related areas, are indebted to these organizations. We would like to thank Lamberto Rondoni, in the graduate program at Virginia Tech, for proofreading manuscripts of all the Italian contributors.
After the book "Basic operatortheory" by Gohberg-Goldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of clas...
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ISBN:
(数字)9783034875097
ISBN:
(纸本)9783034875110
After the book "Basic operatortheory" by Gohberg-Goldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes - the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic operatortheory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first.
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