Reproducing And Pseudo Reproducing Kernels And Their Application To The Partial Differential Equations Of Physics


Reproducing And Pseudo Reproducing Kernels And Their Application To The Partial Differential Equations Of Physics
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Reproducing And Pseudo Reproducing Kernels And Their Application To The Partial Differential Equations Of Physics


Reproducing And Pseudo Reproducing Kernels And Their Application To The Partial Differential Equations Of Physics
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Author : Nachman Aronszajn
language : en
Publisher:
Release Date : 1948

Reproducing And Pseudo Reproducing Kernels And Their Application To The Partial Differential Equations Of Physics written by Nachman Aronszajn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with Differential equations categories.




Kernel Functions And Elliptic Differential Equations In Mathematical Physics


Kernel Functions And Elliptic Differential Equations In Mathematical Physics
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Author : Stefan Bergman
language : en
Publisher: Courier Corporation
Release Date : 2013-01-23

Kernel Functions And Elliptic Differential Equations In Mathematical Physics written by Stefan Bergman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-23 with Mathematics categories.


Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.



Construction And Applications Of Conformal Maps


Construction And Applications Of Conformal Maps
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Author : Institute for Numerical Analysis (U.S.)
language : en
Publisher:
Release Date : 1952

Construction And Applications Of Conformal Maps written by Institute for Numerical Analysis (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Computers categories.




Kernel Functions And Differential Equations


Kernel Functions And Differential Equations
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Author :
language : en
Publisher: Academic Press
Release Date : 2009-08-31

Kernel Functions And Differential Equations written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-31 with Mathematics categories.


Kernel Functions and Differential Equations



Theory Of Reproducing Kernels And Applications


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 Kernel Function And Conformal Mapping


The Kernel Function And Conformal Mapping
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Author : Stefan Bergman
language : en
Publisher: American Mathematical Soc.
Release Date : 1950

The Kernel Function And Conformal Mapping written by Stefan Bergman 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 1950 with Mathematics categories.


The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of ""The Kernel Function"". The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.



Advanced Complex Analysis A Comprehensive Course In Analysis Part 2b


Advanced Complex Analysis A Comprehensive Course In Analysis Part 2b
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-11-02

Advanced Complex Analysis A Comprehensive Course In Analysis Part 2b written by Barry Simon 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 2015-11-02 with Mathematical analysis categories.


A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2B provides a comprehensive look at a number of subjects of complex analysis not included in Part 2A. Presented in this volume are the theory of conformal metrics (including the Poincaré metric, the Ahlfors-Robinson proof of Picard's theorem, and Bell's proof of the Painlevé smoothness theorem), topics in analytic number theory (including Jacobi's two- and four-square theorems, the Dirichlet prime progression theorem, the prime number theorem, and the Hardy-Littlewood asymptotics for the number of partitions), the theory of Fuschian differential equations, asymptotic methods (including Euler's method, stationary phase, the saddle-point method, and the WKB method), univalent functions (including an introduction to SLE), and Nevanlinna theory. The chapters on Fuschian differential equations and on asymptotic methods can be viewed as a minicourse on the theory of special functions.



Variational Methods For Eigenvalue Problems


Variational Methods For Eigenvalue Problems
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Author : S. H. Gould
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24

Variational Methods For Eigenvalue Problems written by S. H. Gould and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Science categories.


Purely mathematical treatment offers simple exposition of general theory of variational methods with special reference to the vibrating plate. No math beyond basic calculus. Includes exercises. 1957 edition.



Reproducing Kernel Hilbert Spaces


Reproducing Kernel Hilbert Spaces
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Author : Howard L. Weinert
language : en
Publisher:
Release Date : 1982

Reproducing Kernel Hilbert Spaces written by Howard L. Weinert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.




Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications


Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications
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Author : A. Weinstein
language : en
Publisher: Elsevier
Release Date : 1972-06-23

Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications written by A. Weinstein and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-23 with Mathematics categories.


In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering