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Author: Tomas I︠A︡kovlevich Azizov
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
An introduction to the geometry of spaces, this research monograph develops the foundations of the theory of linear operators in these spaces and examines the theory of invariant subspaces, spectral questions and the question of the extension of operators.
Author: Tomas I︠A︡kovlevich Azizov
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 328
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Book Description
An introduction to the geometry of spaces, this research monograph develops the foundations of the theory of linear operators in these spaces and examines the theory of invariant subspaces, spectral questions and the question of the extension of operators.
Author: I. S. Iohvidov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112735994
Category : Mathematics
Languages : en
Pages : 120
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Book Description
No detailed description available for "Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric".
Author: J. Bognar
Publisher: Springer Science & Business Media
ISBN: 364265567X
Category : Mathematics
Languages : en
Pages : 235
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Book Description
By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L. Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J.
Author: Henry Helson
Publisher: Birkhäuser
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 384
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Book Description
Author: Israel Gohberg
Publisher: Birkhäuser
ISBN: 3034879806
Category : Mathematics
Languages : en
Pages : 428
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Book Description
A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
Author: Aad Dijksma
Publisher: Birkhäuser
ISBN: 3034888120
Category : Mathematics
Languages : en
Pages : 419
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Book Description
This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday. The book begins with his biography and list of publications. It contains a selection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential equations. Other papers deal with time-varying systems, interpolation and factorization problems, and topics from mathematical physics. About half of the papers contain further developments in the theory of operators in spaces with an indefinite metric and treat new applications. The book is of interest to a wide audience of pure and applied mathematicians.
Author: G. Arsene
Publisher: Birkhäuser
ISBN: 303487250X
Category : Science
Languages : en
Pages : 344
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Book Description
The Operator Theory conferences, organized by the Department of Mathematics of INCREST and the Department of Mathematics of the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operator theory. This book comprises carefully selected papers on theory of linear operators and related fields. Original results of new research in fast developing areas are included. Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are presented. The research contacts of the Department of :viathematics of INCREST with the National Committee for Science and Technology of Romania provided means for developing the research activity in mathematics; they represent the generous framework of these meetings too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for this exellent job.
Author: Matthias Langer
Publisher: Springer Science & Business Media
ISBN: 3764375167
Category : Mathematics
Languages : en
Pages : 403
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Book Description
A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.
Author: Nelson Dunford
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 880
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Book Description
Author: Takayuki Furuta
Publisher: CRC Press
ISBN: 9780415267991
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developments in bounded linear operators.
