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Inner Product Spaces And Applications
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Book Synopsis Partial Inner Product Spaces by : J-P Antoine
Download or read book Partial Inner Product Spaces written by J-P Antoine and published by Springer. This book was released on 2009-12-08 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Characterizations of Inner Product Spaces by : Amir
Download or read book Characterizations of Inner Product Spaces written by Amir and published by Birkhäuser. This book was released on 2013-11-21 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 =
Book Synopsis Inner Product Spaces and Applications by : T M Rassias
Download or read book Inner Product Spaces and Applications written by T M Rassias and published by CRC Press. This book was released on 1997-10-08 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Linear Algebra Done Right by : Sheldon Axler
Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Book Synopsis Semi-inner Products and Applications by : Sever Silvestru Dragomir
Download or read book Semi-inner Products and Applications written by Sever Silvestru Dragomir and published by Nova Biomedical Books. This book was released on 2004 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semi-inner products, that can be naturally defined in general Banach spaces over the real or complex number field, play an important role in describing the geometric properties of these spaces. This new book dedicates 17 chapters to the study of semi-inner products and its applications. The bibliography at the end of each chapter contains a list of the papers cited in the chapter. The interested reader may find more information on the subject by consulting the list of papers provided at the end of the work. The book is intended for use by both researchers and postgraduate students interested in functional analysis. It also provides helpful tools to mathematicians using functional analysis in other domains such as: linear and non-linear operator theory, optimization theory, game theory or other related fields.
Book Synopsis Best Approximation in Inner Product Spaces by : Frank R. Deutsch
Download or read book Best Approximation in Inner Product Spaces written by Frank R. Deutsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra.
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 From Vector Spaces to Function Spaces by : Yutaka Yamamoto
Download or read book From Vector Spaces to Function Spaces written by Yutaka Yamamoto and published by SIAM. This book was released on 2012-10-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.
Book Synopsis Norm Derivatives and Characterizations of Inner Product Spaces by : Claudi Alsina
Download or read book Norm Derivatives and Characterizations of Inner Product Spaces written by Claudi Alsina and published by World Scientific. This book was released on 2010 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Introduction. 1.1. Historical notes. 1.2. Normed linear spaces. 1.3. Strictly convex normed linear spaces. 1.4. Inner product spaces. 1.5. Orthogonalities in normed linear spaces -- 2. Norm derivatives. 2.1. Norm derivatives : Definition and basic properties. 2.2. Orthogonality relations based on norm derivatives. 2.3. p'[symbol]-orthogonal transformations. 2.4. On the equivalence of two norm derivatives. 2.5. Norm derivatives and projections in normed linear spaces. 2.6. Norm derivatives and Lagrange's identity in normed linear spaces. 2.7. On some extensions of the norm derivatives. 2.8. p-orthogonal additivity -- 3. Norm derivatives and heights. 3.1. Definition and basic properties. 3.2. Characterizations of inner product spaces involving geometrical properties of a height in a triangle. 3.3. Height functions and classical orthogonalities. 3.4. A new orthogonality relation. 3.5. Orthocenters. 3.6. A characterization of inner product spaces involving an isosceles trapezoid property. 3.7. Functional equations of the height transform -- 4. Perpendicular bisectors in Normed spaces. 4.1. Definitions and basic properties. 4.2. A new orthogonality relation. 4.3. Relations between perpendicular bisectors and classical orthogonalities. 4.4. On the radius of the circumscribed circumference of a triangle. 4.5. Circumcenters in a triangle. 4.6. Euler line in real normed space. 4.7. Functional equation of the perpendicular bisector transform -- 5. Bisectrices in real Normed spaces. 5.1. Bisectrices in real normed spaces. 5.2. A new orthogonality relation. 5.3. Functional equation of the bisectrix transform. 5.4. Generalized bisectrices in strictly convex real normed spaces. 5.5. Incenters and generalized bisectrices -- 6. Areas of triangles in Normed spaces. 6.1. Definition of four areas of triangles. 6.2. Classical properties of the areas and characterizations of inner product spaces. 6.3. Equalities between different area functions. 6.4. The area orthogonality.
Book Synopsis Theory of 2-inner Product Spaces by : Yeol Je Cho
Download or read book Theory of 2-inner Product Spaces written by Yeol Je Cho and published by Nova Publishers. This book was released on 2001 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky
Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1021 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Book Synopsis Linear Algebra: Inner Product Spaces by : N.B. Singh
Download or read book Linear Algebra: Inner Product Spaces written by N.B. Singh and published by N.B. Singh. This book was released on with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Linear Algebra: Inner Product Spaces" is a comprehensive introductory guide designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra within the context of inner product spaces. This book provides clear explanations and practical examples to facilitate understanding of vectors, matrices, orthogonality, projections, and their applications across diverse fields such as quantum mechanics, signal processing, and machine learning. With an emphasis on accessibility and relevance, it equips readers with essential tools to comprehend and apply linear algebra in solving real-world problems and advancing their mathematical proficiency.
Book Synopsis Advances in Multivariate Statistical Analysis by : Arjun K. Gupta
Download or read book Advances in Multivariate Statistical Analysis written by Arjun K. Gupta and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The death of Professor K.C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog nition of his many contributions in multivariate statis tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T.C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J.D. Knoke, W.J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D.K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.
Book Synopsis Elements of Hilbert Spaces and Operator Theory by : Harkrishan Lal Vasudeva
Download or read book Elements of Hilbert Spaces and Operator Theory written by Harkrishan Lal Vasudeva and published by Springer. This book was released on 2017-03-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.
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 364 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 Metrics, Norms, Inner Products, and Operator Theory by : Christopher Heil
Download or read book Metrics, Norms, Inner Products, and Operator Theory written by Christopher Heil and published by Birkhäuser. This book was released on 2018-08-28 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students. Key features: Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter. Suitable for undergraduate-level courses; no familiarity with measure theory is required. Extensive exercises complement the text and provide opportunities for learning by doing. A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.
