Theory Of Reproducing Kernels And Its Applications
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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.
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.
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.
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."
Complex Analysis And Its Applications
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Author : C.C. Yang
language : en
Publisher: CRC Press
Release Date : 1994-04-05
Complex Analysis And Its Applications written by C.C. Yang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-05 with Mathematics categories.
This volume presents a collection of contributions to an international conference on complex analysis and its applications held at the newly founded Hong Kong University of Science and Technology in January 1993. The aim of the conference was to advance the theoretical aspects of complex analysis and to explore the application of its techniques to physical and engineering problems. Three main areas were emphasised: Value distribution theory; Complex dynamical system and geometric function theory; and the Application of complex analysis to differential quations and physical engineering problems.
Progress In Holomorphic Dynamics
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Author : Hartje Kriete
language : en
Publisher: CRC Press
Release Date : 1998-05-20
Progress In Holomorphic Dynamics written by Hartje Kriete and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-20 with Mathematics categories.
In the last few decades, complex dynamical systems have received widespread public attention and emerged as one of the most active fields of mathematical research. Starting where other monographs in the subject end, Progress in Holomorphic Dynamics advances the theoretical aspects and recent results in complex dynamical systems, with particular emphasis on Siegel discs. Organized into four parts, the papers in this volume grew out of three workshops: two hosted by the Georg-August-Universität Göttingen and one at the "Mathematisches Forschungsinstitut Oberwolfach." Part I addresses linearization. The authors review Yoccoz's proof that the Brjuno condition is the optimal condition for linearizability of indifferent fixed points and offer a treatment of Perez-Marco's refinement of Yoccoz's work. Part II discusses the conditions necessary for the boundary of a Siegel disc to contain a critical point, builds upon Herman's work, and offers a survey of the state-of-the-art regarding the boundaries of Siegel discs. Part III deals with the topology of Julia sets with Siegel discs and contains a remarkable highlight: C.L. Petersen establishes the existence of Siegel discs of quadratic polynomials with a locally connected boundary. Keller, taking a different approach, explains the relations between locally connected "real Julia sets" with Siegel discs and the abstract concepts of kneading sequences and itineraries. Part IV closes the volume with four papers that review the different directions of present research in iteration theory. It includes discussions on the relations between commuting rational functions and their Julia sets, interactions between the iteration of polynomials and the iteration theory of entire transcendental functions, a deep analysis of the topology of the limbs of the Mandelbrot set, and an overview of complex dynamics in higher dimensions.
Singularities Of Solutions Of Second Order Quasilinear Equations
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Author : Laurent Veron
language : en
Publisher: CRC Press
Release Date : 1996-08-01
Singularities Of Solutions Of Second Order Quasilinear Equations written by Laurent Veron and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-01 with Mathematics categories.
This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.
Dirac Operators In Analysis
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Author : John Ryan
language : en
Publisher: CRC Press
Release Date : 1999-01-06
Dirac Operators In Analysis written by John Ryan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-06 with Mathematics categories.
Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.
Integral Expansions Related To Mehler Fock Type Transforms
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Author : B N Mandal
language : en
Publisher: CRC Press
Release Date : 2020-11-25
Integral Expansions Related To Mehler Fock Type Transforms written by B N Mandal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.
An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.