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Author: Daniel Alpay
Publisher: Springer Science & Business Media
ISBN: 9783764300685
Category : Mathematics
Languages : en
Pages : 370
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Book Description
The notions of positive functions and of reproducing kernel Hilbert spaces play an important role in various fields of mathematics, such as stochastic processes, linear systems theory, operator theory, and the theory of analytic functions. Also they are relevant for many applications, for example to statistical learning theory and pattern recognition. The present volume contains a selection of papers which deal with different aspects of reproducing kernel Hilbert spaces. Topics considered include one complex variable theory, differential operators, the theory of self-similar systems, several complex variables, and the non-commutative case. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
Author: Saburou Saitoh
Publisher: Springer
ISBN: 9811005303
Category : Mathematics
Languages : en
Pages : 464
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Book Description
This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.
Author: Vern I. Paulsen
Publisher: Cambridge University Press
ISBN: 1107104092
Category : Mathematics
Languages : en
Pages : 193
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Book Description
A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
Author: Alain Berlinet
Publisher: Springer Science & Business Media
ISBN: 1441990968
Category : Business & Economics
Languages : en
Pages : 369
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Book Description
The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.
Author: Saburou Saitoh
Publisher: Longman
ISBN:
Category : Mathematics
Languages : en
Pages : 180
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Book Description
Author: Gohberg
Publisher: Birkhäuser
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 336
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Book Description
Author: Howard L. Weinert
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 680
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Book Description
Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3034889089
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.
Author: Minggen Cui
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 248
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Book Description
Although the application of reproducing kernel has been explored in different fields in the past twenty to thirty years and the relevant researches are active in the recent five years, there is still not a book on the application of reproducing kernel. This book attempts to introduce to the readers engaged in mathematical application these solutions, especially the constructing theory of the reproducing kernel space that the authors originally created and gradually improved. Reproducing kernel space is a special Hilbert space. the authors have been engaged in the constructing theory research of the reproducing kernel space since 1980's, and worked out a series of specific structural methods for reproducing kernel space and reproducing kernel functions.
Author: Saburou Saitoh
Publisher: CRC Press
ISBN: 1000158047
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Author: Krikamol Muandet
Publisher:
ISBN: 9781680832884
Category : Computers
Languages : en
Pages : 154
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Book Description
Provides a comprehensive review of kernel mean embeddings of distributions and, in the course of doing so, discusses some challenging issues that could potentially lead to new research directions. The targeted audience includes graduate students and researchers in machine learning and statistics.
