Theory Of Reproducing Kernels And Applications

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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.

Reproducing Kernels And Their Applications

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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.

Theory Of Reproducing Kernels And Its Applications

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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.

Selected Papers On Analysis And Differential Equations

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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

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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.

Functional Calculus

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Author : Kamal Shah
language : en
Publisher: BoD – Books on Demand
Release Date : 2020-06-17

Functional Calculus written by Kamal Shah and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-17 with Mathematics categories.

The aim of this book is to present a broad overview of the theory and applications related to functional calculus. The book is based on two main subject areas: matrix calculus and applications of Hilbert spaces. Determinantal representations of the core inverse and its generalizations, new series formulas for matrix exponential series, results on fixed point theory, and chaotic graph operations and their fundamental group are contained under the umbrella of matrix calculus. In addition, numerical analysis of boundary value problems of fractional differential equations are also considered here. In addition, reproducing kernel Hilbert spaces, spectral theory as an application of Hilbert spaces, and an analysis of PM10 fluctuations and optimal control are all contained in the applications of Hilbert spaces. The concept of this book covers topics that will be of interest not only for students but also for researchers and professors in this field of mathematics. The authors of each chapter convey a strong emphasis on theoretical foundations in this book.

The State Space Method

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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006

The State Space Method written by Daniel Alpay 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 2006 with Language Arts & Disciplines categories.

The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists.

A Survey Of Preconditioned Iterative Methods

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Author : Are Magnus Bruaset
language : en
Publisher: Routledge
Release Date : 2018-12-13

A Survey Of Preconditioned Iterative Methods written by Are Magnus Bruaset and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-13 with Mathematics categories.

The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w

A Method For Computing Unsteady Flows In Porous Media

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Author : R Raghavan
language : en
Publisher: Routledge
Release Date : 2017-11-22

A Method For Computing Unsteady Flows In Porous Media written by R Raghavan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

Self-contained and concise, this Research Note provides a basis to study unsteady flow in saturated porous media. It provides for the development of algorithms that examine three-dimensional flows subject to complicated boundary conditions that are a natural consequence of flow in geological systems. A new way to understand the flow in porous media is presented. The authors pay attention to computational considerations, and options for developing codes are addressed. The note consists of five chapters: the first is introductory; the second and third are devoted to showing how one arrives at the solutions of interest; the fourth chapter presents various reformulations to aid computations and presents a few illustrative examples; the fifth chapter is a natural progression of the first four chapters to more complicated visualizations of flow in porous media.

Conjugate Gradient Type Methods For Ill Posed Problems

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Author : Martin Hanke
language : en
Publisher: Routledge
Release Date : 2017-11-22

Conjugate Gradient Type Methods For Ill Posed Problems written by Martin Hanke and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.