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Indefinite Inner Product Spaces
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Book Synopsis Indefinite Inner Product Spaces by : J. Bognar
Download or read book Indefinite Inner Product Spaces written by J. Bognar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics.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.
Book Synopsis Indefinite Linear Algebra and Applications by : Israel Gohberg
Download or read book Indefinite Linear Algebra and Applications written by Israel Gohberg and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.
Book Synopsis Indefinite Inner Product Spaces by : Janos Bognar
Download or read book Indefinite Inner Product Spaces written by Janos Bognar and published by . This book was released on 1974 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Operator Theory and Indefinite Inner Product Spaces by : Matthias Langer
Download or read book Operator Theory and Indefinite Inner Product Spaces written by Matthias Langer and published by Springer Science & Business Media. This book was released on 2006-06-16 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations by : Daniel Alpay
Download or read book Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations written by Daniel Alpay and published by Birkhäuser. This book was released on 2018-01-30 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer’s chief research interests and will appeal to a broad readership whose work involves operator theory.
Book Synopsis Operator Theory in Inner Product Spaces by : Karl-Heinz Förster
Download or read book Operator Theory in Inner Product Spaces written by Karl-Heinz Förster and published by Springer Science & Business Media. This book was released on 2007-03-20 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Indefinite Linear Algebra and Applications by : Israel Gohberg
Download or read book Indefinite Linear Algebra and Applications written by Israel Gohberg and published by Springer. This book was released on 2005-10-18 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.
Book Synopsis Inner Product Structures by : V.I. Istratescu
Download or read book Inner Product Structures written by V.I. Istratescu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 909 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis An Indefinite Excursion in Operator Theory by : Aurelian Gheondea
Download or read book An Indefinite Excursion in Operator Theory written by Aurelian Gheondea and published by Cambridge University Press. This book was released on 2022-07-28 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
Book Synopsis Linear Operators in Spaces with an Indefinite Metric by : Tomas I︠A︡kovlevich Azizov
Download or read book Linear Operators in Spaces with an Indefinite Metric written by Tomas I︠A︡kovlevich Azizov and published by . This book was released on 1989-10-27 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Symmetric Bilinear Forms by : John Milnor
Download or read book Symmetric Bilinear Forms written by John Milnor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory cf quadratic forms and the intimately related theory of sym metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse. (Compare [Dickson] and [Bourbaki, 24, p. 185].) Our exposition will concentrate on the rela tively recent developments which begin with and are inspired by Witt's 1937 paper "Theorie der quadratischen Formen in beliebigen Körpern." We will be particularly interested in the work of A. Pfister and M. Knebusch. However, some older material will be described, particularly in Chapter II. The presentation is based on lectures by Milnor at the Institute for Ad vanced Study, and at Haverford College under the Phillips Lecture Pro gram, during the Fall of 1970, as weIl as Iectures at Princeton University il1 1966. We want to thank J. Cunningham, M. Knebusch, M. Kneser, A. Rosenberg, W. Scharlau and J.-P. Serre for helpful suggestions and corrections. Prerequisites. The reader should be familiar with the rudiments of algebra., incJuding for example the concept of tensor product for mo dules over a commutative ring. A few individual sections will require quite a bit more. The logical relationship between the various chapters can be roughly described by the diagram below. There are also five appendices, largely self-contained, which treat special topics. I. Arbitrary commutative rings I H. The ring of V. Miscellaneous IIl. Fields integers examples IV. Dedekind domains Contents Chapter r. Basie Coneepts ...
Book Synopsis Spectral Theory in Inner Product Spaces and Applications by : Jussi Behrndt
Download or read book Spectral Theory in Inner Product Spaces and Applications written by Jussi Behrndt and published by Springer Science & Business Media. This book was released on 2009-01-21 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a collection of research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17. This work discusses topics such as linear relations, singular perturbations, de Branges spaces, nonnegative matrices, and abstract kinetic equations.
Book Synopsis Topics in Quaternion Linear Algebra by : Leiba Rodman
Download or read book Topics in Quaternion Linear Algebra written by Leiba Rodman and published by Princeton University Press. This book was released on 2014-08-24 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.
Book Synopsis Operator Theory and Indefinite Inner Product Spaces by : Matthias Langer
Download or read book Operator Theory and Indefinite Inner Product Spaces written by Matthias Langer and published by Birkhäuser. This book was released on 2009-09-03 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Toeplitz Operators and Related Topics by : Estelle L. Basor
Download or read book Toeplitz Operators and Related Topics written by Estelle L. Basor and published by Birkhäuser. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Harold Widom, a distinguished mathematician and renowned expert in the area of Toeplitz, Wiener-Hopf and pseudodifferential operators, on the occasion of his sixtieth birthday. The book opens with biographical material and a list of the mathematician's publications, this being followed by two papers based on Toeplitz lectures which he delivered at Tel Aviv University in March, 1993. The rest of the book consists of a selection of papers containing some recent achievements in the following areas: Szegö-Widom asymptotic formulas for determinants of finite sections of Toeplitz matrices and their generalizations, the Fisher-Hartwig conjecture, random matrices, analysis of kernels of Toeplitz matrices, projectional methods and eigenvalue distribution for Toeplitz matrices, the Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorff type theorems. The book will appeal to a wide audience of pure and applied mathematicians.
Book Synopsis Combinatorial Matrix Theory and Generalized Inverses of Matrices by : Ravindra B. Bapat
Download or read book Combinatorial Matrix Theory and Generalized Inverses of Matrices written by Ravindra B. Bapat and published by Springer Science & Business Media. This book was released on 2013-02-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.
Book Synopsis Theory and Applications of Volterra Operators in Hilbert Space by : Israel Gohberg
Download or read book Theory and Applications of Volterra Operators in Hilbert Space written by Israel Gohberg and published by American Mathematical Soc.. This book was released on with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: An abstract Volterra operator is, roughly speaking, a compact operator in a Hilbert space whose spectrum consists of a single point $\lambda=0$. The theory of abstract Volterra operators, significantly developed by the authors of the book and their collaborators, represents an important part of the general theory of non-self-adjoint operators in Hilbert spaces. The book, intended for all mathematicians interested in functional analysis and its applications, discusses the main ideas and results of the theory of abstract Volterra operators. Of particular interest to analysts and specialists in differential equations are the results about analytic models of abstract Volterra operators and applications to boundary value problems for ordinary differential equations.
