Positive Definite and Definitizable Functions PDF Download
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Author: Zoltán Sasvári
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 216
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Book Description
Author: Zoltán Sasvári
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 216
Get Book Here
Book Description
Author: Rajendra Bhatia
Publisher: Princeton University Press
ISBN: 0691168253
Category : Mathematics
Languages : en
Pages : 264
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Book Description
This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.
Author: Torben Maack Bisgaard
Publisher: Nova Publishers
ISBN: 9781560728603
Category : Mathematics
Languages : en
Pages : 152
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Book Description
This book contains basic information on characteristic functions and moment sequences that is frequently used in probability theory. Characteristic functions and moment sequences are viewed as special cases of positive definite functions. Positive definite functions occur in diverse parts of mathematics, e.g. in operator theory, moment problems, complex function theory, embedding problems, integral equations, and other areas. However, the area of mathematics in which the largest number of people use positive definite functions (some without knowing it) seems to be that of probability theory.
Author: Joseph A. Ball
Publisher: Springer Science & Business Media
ISBN: 3034601581
Category : Mathematics
Languages : en
Pages : 624
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Book Description
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.
Author: Zoltán Sasvári
Publisher: Walter de Gruyter
ISBN: 3110223996
Category : Mathematics
Languages : en
Pages : 376
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Book Description
In a certain sense characteristic functions and correlation functions are the same, the common underlying concept is positive definiteness. Many results in probability theory, mathematical statistics and stochastic processes can be derived by using these functions. While there are books on characteristic functions of one variable, books devoting some sections to the multivariate case, and books treating the general case of locally compact groups, interestingly there is no book devoted entirely to the multidimensional case which is extremely important for applications. This book is intended to fill this gap at least partially. It makes the basic concepts and results on multivariate characteristic and correlation functions easily accessible to both students and researchers in a comprehensive manner. The first chapter presents basic results and should be read carefully since it is essential for the understanding of the subsequent chapters. The second chapter is devoted to correlation functions, their applications to stationary processes and some connections to harmonic analysis. In Chapter 3 we deal with several special properties, Chapter 4 is devoted to the extension problem while Chapter 5 contains a few applications. A relatively large appendix comprises topics like infinite products, functional equations, special functions or compact operators.
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: Elliott Ward Cheney
Publisher: American Mathematical Soc.
ISBN: 0821847988
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.
Author: Vadim Adamyan
Publisher: Springer Science & Business Media
ISBN: 3764399198
Category : Mathematics
Languages : en
Pages : 497
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Book Description
This is the first of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.
Author: Niels Jacob
Publisher: World Scientific
ISBN: 178326134X
Category : Mathematics
Languages : en
Pages : 517
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Book Description
After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students./a
Author: Werner Kratz
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 304
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Book Description
This monograph is intended to provide classical and recent results on quadratic functionals. On the one hand it contains the well-known facts on the second variation from the calculus of variations, including Jacobi-type conditions, and on the other hand new aspects in control theory, in particular the notion of strong observability and its relation to the optimal linear regulator. The main object described is a general theory of self-adjoint eigenvalue problems for linear Hamiltonian systems, which includes Morse's oscillation theory and his extensions of Sturmian theory. The dependence on the eigenvalue parameter may be nonlinear. The treatment is based on a novel approach via field theory, in particular Picone's identity. The central features needed for the method are recent results on Riccati matrix differential equations and on monotone matrix-valued functions. Applications of the theory yield classical and new results in such areas as, for example, linear control theory, variational analysis (Rayleigh's principle), or Sturm-Liouville eigenvalue problems. The book is self-contained, and accessible to mathematics or science students entering the graduate level.
