Reproducing Kernel Spaces And Applications

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Reproducing Kernel Spaces And Applications

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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Reproducing Kernel Spaces And Applications written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

20. Pattern recognition and statistical learning theory (the theory of support vector machines). See [40], [58]. In this last volume we refer in particular to the papers [63] and [64]. Since this topic is maybe less known to the operator theory community we mention that the support vector method is a general approach to function estimation problems. See [63, p. 26]. We note that the above list and the given references are by no way exhaustive. We refer to the first section of the paper of S. Saitoh in the present volume for another (and mainly different) list of topics where reproducing kernel spaces appear. Quite often a given question is best understood in a reproducing kernel Hilbert space (for instance when using Cauchy's formula in the Hardy space H ) 2 and one finds oneself as Mr Jourdain of Moliere' Bourgeois Gentilhomme speaking Prose without knowing it [48, p. 51]: Par ma foil il y a plus de quarante ans que je dis de la prose sans que l j'en susse rien.

Reproducing Kernel Hilbert Spaces In Probability And Statistics

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Author : Alain Berlinet
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28

Reproducing Kernel Hilbert Spaces In Probability And Statistics written by Alain Berlinet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Business & Economics categories.

The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel (gaussian processes) with a Hilbert space offunctions. Like all transform theories (think Fourier), problems in one space may become transparent in the other, and optimal solutions in one space are often usefully optimal in the other. The theory was born in complex function theory, abstracted and then accidently injected into Statistics; Manny Parzen as a graduate student at Berkeley was given a strip of paper containing his qualifying exam problem- It read "reproducing kernel Hilbert space"- In the 1950's this was a truly obscure topic. Parzen tracked it down and internalized the subject. Soon after, he applied it to problems with the following fla vor: consider estimating the mean functions of a gaussian process. The mean functions which cannot be distinguished with probability one are precisely the functions in the Hilbert space associated to the covariance kernel of the processes. Parzen's own lively account of his work on re producing kernels is charmingly told in his interview with H. Joseph Newton in Statistical Science, 17, 2002, p. 364-366. Parzen moved to Stanford and his infectious enthusiasm caught Jerry Sacks, Don Ylvisaker and Grace Wahba among others. Sacks and Ylvis aker applied the ideas to design problems such as the following. Sup pose (XdO

Reproducing Kernel Hilbert Spaces

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Author : Howard L. Weinert
language : en
Publisher:
Release Date : 1982

Reproducing Kernel Hilbert Spaces written by Howard L. Weinert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.

Theory Of Reproducing Kernels And Applications

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Author : Saburou Saitoh
language : en
Publisher: Springer
Release Date : 2016-10-14

Theory Of Reproducing Kernels And Applications written by Saburou Saitoh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-14 with Mathematics categories.

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.

Integral Transforms Reproducing Kernels And Their Applications

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Author : Saburou Saitoh
language : en
Publisher: CRC Press
Release Date : 1997-05-28

Integral Transforms Reproducing Kernels And Their Applications written by Saburou Saitoh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-28 with Mathematics categories.

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.

The Schur Algorithm Reproducing Kernel Spaces And System Theory

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Author : Daniel Alpay
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

The Schur Algorithm Reproducing Kernel Spaces And System Theory written by Daniel Alpay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.

Looks at matrix-valued Schur functions and their applications from the unifying point of view of space with reproducing kernels to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. Chapters cover reproducing kernel spaces, theory of linear systems, the Schur algorithm and the inverse scattering problem, operator models, interpolation, the indefinite case, the non-stationary case, and Riemann surfaces. Originally published in French by Societe Mathematique de France, 1998. Translated from the French by Stephen S. Wilson. Author information is not given. c. Book News Inc.

Kernel Mean Embedding Of Distributions

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Author : Krikamol Muandet
language : en
Publisher:
Release Date : 2017-06-28

Kernel Mean Embedding Of Distributions written by Krikamol Muandet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-28 with Computers categories.

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.

Pick Interpolation And Hilbert Function Spaces

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Author : Jim Agler
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Pick Interpolation And Hilbert Function Spaces written by Jim Agler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^\infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^\infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Hilbert Space Methods In Signal Processing

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Author : Rodney A. Kennedy
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-07

Hilbert Space Methods In Signal Processing written by Rodney A. Kennedy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.

An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.

Kernels For Vector Valued Functions

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Author : Mauricio A. Álvarez
language : en
Publisher: Foundations & Trends
Release Date : 2012

Kernels For Vector Valued Functions written by Mauricio A. Álvarez and has been published by Foundations & Trends this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.

This monograph reviews different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and regularization methods.