Reproducing Kernel Spaces and Applications

Reproducing Kernel Spaces and Applications
Title Reproducing Kernel Spaces and Applications PDF eBook
Author Daniel Alpay
Publisher Birkhäuser
Pages 355
Release 2012-12-06
Genre Mathematics
ISBN 3034880774

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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.

Reproducing Kernel Spaces and Applications

Reproducing Kernel Spaces and Applications
Title Reproducing Kernel Spaces and Applications PDF eBook
Author Daniel Alpay
Publisher Springer Science & Business Media
Pages 370
Release 2003-08-29
Genre Mathematics
ISBN 9783764300685

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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.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
Title An Introduction to the Theory of Reproducing Kernel Hilbert Spaces PDF eBook
Author Vern I. Paulsen
Publisher Cambridge University Press
Pages 193
Release 2016-04-11
Genre Mathematics
ISBN 1107104092

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A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.

Theory of Reproducing Kernels and Applications

Theory of Reproducing Kernels and Applications
Title Theory of Reproducing Kernels and Applications PDF eBook
Author Saburou Saitoh
Publisher Springer
Pages 0
Release 2016-10-27
Genre Mathematics
ISBN 9789811005299

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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.

Reproducing Kernel Hilbert Spaces in Probability and Statistics

Reproducing Kernel Hilbert Spaces in Probability and Statistics
Title Reproducing Kernel Hilbert Spaces in Probability and Statistics PDF eBook
Author Alain Berlinet
Publisher Springer Science & Business Media
Pages 369
Release 2011-06-28
Genre Business & Economics
ISBN 1441990968

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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.

Theory of Reproducing Kernels and Its Applications

Theory of Reproducing Kernels and Its Applications
Title Theory of Reproducing Kernels and Its Applications PDF eBook
Author Saburou Saitoh
Publisher Longman
Pages 180
Release 1988
Genre Mathematics
ISBN

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Reproducing Kernel Hilbert Spaces

Reproducing Kernel Hilbert Spaces
Title Reproducing Kernel Hilbert Spaces PDF eBook
Author Howard L. Weinert
Publisher
Pages 680
Release 1982
Genre Mathematics
ISBN

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