Reproducing Kernels And Their Applications

Author : Saburou Saitoh
Publisher : CRC Press
ISBN 13 : 1000158047
Total Pages : 300 pages
Book Rating : 4.45/5 ( download)

DOWNLOAD NOW!

Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-26 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Saburou Saitoh
Publisher : Springer
ISBN 13 : 9811005303
Total Pages : 452 pages
Book Rating : 4.05/5 ( download)

DOWNLOAD NOW!

Download or read book Theory of Reproducing Kernels and Applications written by Saburou Saitoh and published by Springer. This book was released on 2016-10-14 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : S. Saitoh
Publisher : Springer Science & Business Media
ISBN 13 : 1475729871
Total Pages : 235 pages
Book Rating : 4.70/5 ( download)

DOWNLOAD NOW!

Download or read book Reproducing Kernels and their Applications written by S. Saitoh and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vern I. Paulsen
Publisher : Cambridge University Press
ISBN 13 : 1107104092
Total Pages : 193 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to the Theory of Reproducing Kernel Hilbert Spaces written by Vern I. Paulsen and published by Cambridge University Press. This book was released on 2016-04-11 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.

Author : Saburou Saitoh
Publisher : CRC Press
ISBN 13 : 1000115240
Total Pages : 289 pages
Book Rating : 4.46/5 ( download)

DOWNLOAD NOW!

Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-25 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Saburou Saitoh
Publisher : Longman
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.48/5 ( download)

DOWNLOAD NOW!

Download or read book Theory of Reproducing Kernels and Its Applications written by Saburou Saitoh and published by Longman. This book was released on 1988 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3034880774
Total Pages : 355 pages
Book Rating : 4.70/5 ( download)

DOWNLOAD NOW!

Download or read book Reproducing Kernel Spaces and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alain Berlinet
Publisher : Springer Science & Business Media
ISBN 13 : 1441990968
Total Pages : 369 pages
Book Rating : 4.69/5 ( download)

DOWNLOAD NOW!

Download or read book Reproducing Kernel Hilbert Spaces in Probability and Statistics written by Alain Berlinet and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : American Mathematical Soc.
ISBN 13 : 9780821821558
Total Pages : 162 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book The Schur Algorithm, Reproducing Kernel Spaces and System Theory written by Daniel Alpay and published by American Mathematical Soc.. This book was released on 2001 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of Schur functions consists of analytic functions on the unit disk that are bounded by $1$. The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering. In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Societe Mathematique de France. Translated by Stephen S. Wilson.

Author : Randy K. Young
Publisher : Springer Science & Business Media
ISBN 13 : 1461535840
Total Pages : 233 pages
Book Rating : 4.43/5 ( download)

DOWNLOAD NOW!

Download or read book Wavelet Theory and Its Applications written by Randy K. Young and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.