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Author | : Saburou Saitoh |
Publisher | : Springer |
Total Pages | : 464 |
Release | : 2016-10-14 |
Genre | : Mathematics |
ISBN | : 9811005303 |
Download Theory of Reproducing Kernels and Applications Book in PDF, ePub and Kindle
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 |
Total Pages | : 193 |
Release | : 2016-04-11 |
Genre | : Mathematics |
ISBN | : 1107104092 |
Download An Introduction to the Theory of Reproducing Kernel Hilbert Spaces Book in PDF, ePub and Kindle
A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
Author | : S. Saitoh |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1475729871 |
Download Reproducing Kernels and their Applications Book in PDF, ePub and Kindle
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.
Author | : Saburou Saitoh |
Publisher | : Longman |
Total Pages | : 180 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : |
Download Theory of Reproducing Kernels and Its Applications Book in PDF, ePub and Kindle
Author | : Alain Berlinet |
Publisher | : Springer Science & Business Media |
Total Pages | : 369 |
Release | : 2011-06-28 |
Genre | : Business & Economics |
ISBN | : 1441990968 |
Download Reproducing Kernel Hilbert Spaces in Probability and Statistics Book in PDF, ePub and Kindle
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 | : Daniel Alpay |
Publisher | : Birkhäuser |
Total Pages | : 355 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034880774 |
Download Reproducing Kernel Spaces and Applications Book in PDF, ePub and Kindle
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 | : Krikamol Muandet |
Publisher | : |
Total Pages | : 154 |
Release | : 2017-06-28 |
Genre | : Computers |
ISBN | : 9781680832884 |
Download Kernel Mean Embedding of Distributions Book in PDF, ePub and Kindle
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.
Author | : Saburou Saitoh |
Publisher | : CRC Press |
Total Pages | : 300 |
Release | : 2020-11-26 |
Genre | : Mathematics |
ISBN | : 1000158047 |
Download Integral Transforms, Reproducing Kernels and Their Applications Book in PDF, ePub and Kindle
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 | : Daniel Alpay |
Publisher | : Birkhäuser |
Total Pages | : 244 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034889089 |
Download Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces Book in PDF, ePub and Kindle
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 | : Jim Agler |
Publisher | : American Mathematical Society |
Total Pages | : 330 |
Release | : 2023-02-22 |
Genre | : Mathematics |
ISBN | : 1470468557 |
Download Pick Interpolation and Hilbert Function Spaces Book in PDF, ePub and Kindle
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.