Reproducing Kernels And Their Applications

Author : S. Saitoh,Daniel Alpay,Joseph A. Ball,Takeo Ohsawa
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 42,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475729870

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Reproducing Kernels and their Applications by S. Saitoh,Daniel Alpay,Joseph A. Ball,Takeo Ohsawa Pdf

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 : CRC Press
Page : 300 pages
File Size : 48,5 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000158045

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Integral Transforms, Reproducing Kernels and Their Applications by Saburou Saitoh Pdf

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,Yoshihiro Sawano
Publisher : Springer
Page : 452 pages
File Size : 54,8 Mb
Release : 2016-10-14
Category : Mathematics
ISBN : 9789811005305

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Theory of Reproducing Kernels and Applications by Saburou Saitoh,Yoshihiro Sawano Pdf

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 : Saburou Saitoh
Publisher : CRC Press
Page : 289 pages
File Size : 42,9 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000115246

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Integral Transforms, Reproducing Kernels and Their Applications by Saburou Saitoh Pdf

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
Page : 355 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880770

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Reproducing Kernel Spaces and Applications by Daniel Alpay Pdf

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 : Saburou Saitoh
Publisher : Longman
Page : 180 pages
File Size : 54,5 Mb
Release : 1988
Category : Mathematics
ISBN : UCAL:B5008548

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Theory of Reproducing Kernels and Its Applications by Saburou Saitoh Pdf

Author : Vern I. Paulsen,Mrinal Raghupathi
Publisher : Cambridge University Press
Page : 193 pages
File Size : 52,6 Mb
Release : 2016-04-11
Category : Mathematics
ISBN : 9781107104099

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An Introduction to the Theory of Reproducing Kernel Hilbert Spaces by Vern I. Paulsen,Mrinal Raghupathi Pdf

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

Author : Daniel Alpay
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 47,7 Mb
Release : 2001
Category : Computers
ISBN : 0821821555

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The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay Pdf

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
Page : 233 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461535843

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Wavelet Theory and Its Applications by Randy K. Young Pdf

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.

Author : Alain Berlinet,Christine Thomas-Agnan
Publisher : Springer Science & Business Media
Page : 369 pages
File Size : 47,6 Mb
Release : 2011-06-28
Category : Business & Economics
ISBN : 9781441990969

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Reproducing Kernel Hilbert Spaces in Probability and Statistics by Alain Berlinet,Christine Thomas-Agnan Pdf

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 : R.S. Pathak
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 53,6 Mb
Release : 2013-11-11
Category : Social Science
ISBN : 9781489915917

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Generalized Functions and Their Applications by R.S. Pathak Pdf

The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.

Author : Peter Ebenfelt,Björn Gustafsson,Dmitry Khavinson,Mihai Putinar
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 41,5 Mb
Release : 2006-03-10
Category : Mathematics
ISBN : 9783764373160

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Quadrature Domains and Their Applications by Peter Ebenfelt,Björn Gustafsson,Dmitry Khavinson,Mihai Putinar Pdf

Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.

Author : V.I. Istratescu
Publisher : Springer Science & Business Media
Page : 909 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400937130

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Inner Product Structures by V.I. Istratescu Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Michael Ruzhansky,Jens Wirth
Publisher : World Scientific
Page : 668 pages
File Size : 40,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814313162

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Progress in Analysis and Its Applications by Michael Ruzhansky,Jens Wirth Pdf

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.

Author : Michael Ruzhansky,Jens Wirth
Publisher : World Scientific
Page : 668 pages
File Size : 44,7 Mb
Release : 2010-07-29
Category : Mathematics
ISBN : 9789814464703

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Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress by Michael Ruzhansky,Jens Wirth Pdf

The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.