Theory Of Reproducing Kernels And Applications

DOWNLOAD

Download Theory Of Reproducing Kernels And Applications PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Theory Of Reproducing Kernels And Applications book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Theory Of Reproducing Kernels And Applications

DOWNLOAD
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.

Reproducing Kernels And Their Applications

DOWNLOAD
Author : S. Saitoh
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-04-30

Reproducing Kernels And Their Applications written by S. Saitoh 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 1999-04-30 with Mathematics categories.

The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997. As specified in the invitation of the President Professor Robert P. Gilbert of the ISAAC, we organized the session on Reproducing Kerneis and Their Applications. In our session, we presented 24 engaging talks on topics of current interest to the research community. As suggested and organized by Professor Gilbert, we hereby publish its Proceedings. Rather than restricting the papers to Congress participants, we asked the Ieading mathematicians in the field of the theory of reproducing kern eIs to submit papers. However, due to time restrietions and a compulsion to limit the Proceedings a reasonable size, we were unable to obtain a comprehensive treatment of the theory of reproducing kernels. Nevertheless, we hope this Proceedings of the First International Conference on reproducing kerneis will become a significant reference volume. Indeed, we believe that the theory of reproducing kernels will stand out as a fundamental and beautiful contribution in mathematical sciences with a broad array of applications to other areas of mathematics and science. We would like to thank Professor Robert Gilbert for his substantial contri bu tions to the Congress and to our Proceedings. We also express our sincere thanks to the staff of the University of Delaware for their manifold cooperation in organizing the Congress.

Reproducing Kernel Hilbert Spaces In Probability And Statistics

DOWNLOAD
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

Integral Transforms Reproducing Kernels And Their Applications

DOWNLOAD
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.

Theory Of Reproducing Kernels And Its Applications

DOWNLOAD
Author : Saburou Saitoh
language : en
Publisher: Longman
Release Date : 1988

Theory Of Reproducing Kernels And Its Applications written by Saburou Saitoh and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Kernel Mean Embedding Of Distributions

DOWNLOAD
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.

Kernels For Vector Valued Functions

DOWNLOAD
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.

Selected Papers On Analysis And Differential Equations

DOWNLOAD
Author : American Mathematical Society
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Selected Papers On Analysis And Differential Equations written by American Mathematical Society 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 2010 with Mathematics categories.

"Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."

The Theory Of Quantaloids

DOWNLOAD
Author : K I Rosenthal
language : en
Publisher: CRC Press
Release Date : 2014-07-22

The Theory Of Quantaloids written by K I Rosenthal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.

This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.

Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory

DOWNLOAD
Author : Palle Jorgensen
language : en
Publisher: World Scientific
Release Date : 2021-01-15

Infinite Dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory written by Palle Jorgensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-15 with Mathematics categories.

The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.