Inner Product Spaces And Applications
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Inner Product Spaces And Applications
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Author : T M Rassias
language : en
Publisher: CRC Press
Release Date : 1997-10-08
Inner Product Spaces And Applications written by T M Rassias and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-08 with Mathematics categories.
In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces. They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied mathematics. The methods employed are accessible to students familiar with normed linear spaces. Some of the theorems presented are at the same time simple and challenging.
Inner Product Structures
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Author : V.I. Istratescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inner Product Structures written by V.I. Istratescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Partial Inner Product Spaces
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Author : J-P Antoine
language : en
Publisher: Springer
Release Date : 2009-12-08
Partial Inner Product Spaces written by J-P Antoine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-08 with Mathematics categories.
Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.
Indefinite Inner Product Spaces Schur Analysis And Differential Equations
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2018-01-30
Indefinite Inner Product Spaces Schur Analysis And Differential Equations written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.
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.
Spectral Theory In Inner Product Spaces And Applications
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Author : Jussi Behrndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-21
Spectral Theory In Inner Product Spaces And Applications written by Jussi Behrndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-21 with Mathematics categories.
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.
Operator Theory In Inner Product Spaces
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Author : Karl-Heinz Förster
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-20
Operator Theory In Inner Product Spaces written by Karl-Heinz Förster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-20 with Mathematics categories.
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.
Theory Of 2 Inner Product Spaces
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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2001
Theory Of 2 Inner Product Spaces written by Yeol Je Cho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The purpose of this book is to give systematic and comprehensive presentation of theory of n-metric spaces, linear n-normed spaces and n-inner product spaces (and so 2-metric spaces, linear 2-normed spaces and 2-linner product spaces n=2). Since 1963 and 1965, S. Gahler published two papers entitled "2-metrische Raume und ihr topologische Strukhur" and "Lineare 2-normierte Raume", a number of authors have done considerable works on geometric structures of 2-metric spaces and linear 2-normed spaces, and have applied these spaces to several fields of mathematics in many ways. In 1969, S. Gahler introduced also the concept of n metric spaces in a series of his papers entitled "Untersuchungen uber verallemeinerte n-metriscke Raume 1, II, III", which extend the concept of 2-metric spaces to the general case, and provided many properties of topological and geometrical structures. Recently, A. Misiak introduced the concept of n-inner product spaces and extended many results in 2 inner product spaces,which in turn were introduced and studied by C. Diminnie, S. Gahler and A. White, to n-inner product spaces in his doctoral dissertation. This book contains, in short, the latest results on 2-metric spaces and linear 2-normed spaces, 2-inner product spaces, G-inner product spaces, strict convexity and uniform convexity, orthogonal relations, quadratic sets on modules and n-inner product spaces. It is hoped that this book will be devoted to a stimulation of interest in further exploration and to the possible applications in various other branches of mathematics.
Norm Derivatives And Characterizations Of Inner Product Spaces
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Author : Claudi Alsina
language : en
Publisher: World Scientific
Release Date : 2010
Norm Derivatives And Characterizations Of Inner Product Spaces written by Claudi Alsina and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. Since the appearance of Jordanvon Neumann's classical theorem (The Parallelogram Law) in 1935, the field of characterizations of inner product spaces has received a significant amount of attention in various literature texts. Moreover, the techniques arising in the theory of functional equations have shown to be extremely useful in solving key problems in the characterizations of Banach spaces as Hilbert spaces. This book presents, in a clear and detailed style, state-of-the-art methods of characterizing inner product spaces by means of norm derivatives. It brings together results that have been scattered in various publications over the last two decades and includes more new material and techniques for solving functional equations in normed spaces. Thus the book can serve as an advanced undergraduate or graduate text as well as a resource book for researchers working in geometry of Banach (Hilbert) spaces or in the theory of functional equations (and their applications).
Characterizations Of Inner Product Spaces
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Author : Amir
language : en
Publisher: Birkhäuser
Release Date : 2013-11-21
Characterizations Of Inner Product Spaces written by Amir and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Science categories.
Every mathematician working in Banaeh spaee geometry or Approximation theory knows, from his own experienee, that most "natural" geometrie properties may faH to hold in a generalnormed spaee unless the spaee is an inner produet spaee. To reeall the weIl known definitions, this means IIx 11 = *, where is an inner (or: scalar) product on E, Le. a function from ExE to the underlying (real or eomplex) field satisfying: (i) O for x o. (ii) is linear in x. (iii) = (intherealease, thisisjust =
Indefinite Linear Algebra And Applications
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Author : Israel Gohberg
language : en
Publisher: Springer
Release Date : 2005-10-18
Indefinite Linear Algebra And Applications written by Israel Gohberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-18 with Mathematics categories.
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.