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Author: Rudy George Svoboda
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 78
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Book Description
Author: Rudy George Svoboda
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 78
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Book Description
Author: Amir
Publisher: Birkhäuser
ISBN: 3034854870
Category : Science
Languages : en
Pages : 205
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Book Description
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 =
Author: Claudi Alsina
Publisher: World Scientific
ISBN: 9814287261
Category : Mathematics
Languages : en
Pages : 199
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Book Description
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).
Author: Vasile I. Istratescu
Publisher: Routledge
ISBN: 1351413333
Category : Mathematics
Languages : en
Pages : 329
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Book Description
This important work provides a comprehensive overview of the properties of Banachspaces related to strict convexity and a survey of significant applications-uniting a wealthof information previously scattered throughout the mathematical literature in a well-organized,accessible format.After introducing the subject through a discussion of the basic results of linear functionalanalysis, this unique book proceeds to investigate the characteristics of strictly convexspaces and related classes, including uniformly convex spaces, and examine important applicationsregarding approximation theory and fixed point theory. Following this extensivetreatment, the book discusses complex strictly convex spaces and related spaces- alsowith applications. Complete, clearly elucidated proofs accompany results throughout thebook, and ample references are provided to aid further research of the subject.Strict Convexity and Complex Strict Convexity is essential fot mathematicians and studentsinterested in geometric theory of Banach spaces and applications to approximationtheory and fixed point theory, and is of great value to engineers working in optimizationstudies. In addition, this volume serves as an excellent text for a graduate course inGeometric Theory of Banach Spaces.
Author: John Arthur Oman
Publisher:
ISBN:
Category : Generalized spaces
Languages : en
Pages : 260
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Book Description
Author: Yeol Je Cho
Publisher: Nova Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 350
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Book Description
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.
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: T M Rassias
Publisher: CRC Press
ISBN: 9780582317116
Category : Mathematics
Languages : en
Pages : 284
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Book Description
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.
Author: Mahlon Marsh Day
Publisher: Springer
ISBN: 366225249X
Category : Mathematics
Languages : en
Pages : 145
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Book Description
This book contains a compressed introduction to the study of normed linear spaces and to that part of the theory of linear topological spaces without which the main discussion could not well proceed. Definitions of many terms which are required in passing can be found in the alphabetical index, page 134. Symbols which are used throughout all, or a significant part, of this book are indexed on page 132. Each reference to the bibliography, page 124, is made by means of the author's name, supplemented when necessary by a number in square brackets. The bibliography does not completely cover the available literature, even the most recent; each paper in it is the subject of a specific reference at some point in the text. The writer takes this opportunity to express thanks to the University of Illinois, the National Science Foundation, and the University of Washington, each of which has contributed in some degree to the cultural, financial, or physical support of the writer, and to Mr. R. R. PHELPS, who eradicated many of the errors with which the manuscript was infested.
Author: V.I. Istratescu
Publisher: Springer Science & Business Media
ISBN: 9789027721822
Category : Mathematics
Languages : en
Pages : 918
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Book Description
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.
