Transformations Transmutations And Kernel Functions
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Transformations Transmutations And Kernel Functions
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Author : H Begehr
language : en
Publisher: CRC Press
Release Date : 1993-09-23
Transformations Transmutations And Kernel Functions written by H Begehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-23 with Mathematics categories.
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Transformations Transmutations And Kernel Functions Volume Ii
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Author : H Begehr
language : en
Publisher: CRC Press
Release Date : 2023-06-16
Transformations Transmutations And Kernel Functions Volume Ii written by H Begehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-16 with Mathematics categories.
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Integral Transforms Reproducing Kernels And Their Applications
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Author : Saburou Saitoh
language : en
Publisher: CRC Press
Release Date : 2020-11-26
Integral Transforms Reproducing Kernels And Their Applications written by Saburou Saitoh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
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.
Transformations Transmutations And Kernel Functions
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Author : Heinrich G. W. Begehr
language : en
Publisher:
Release Date : 2019
Transformations Transmutations And Kernel Functions written by Heinrich G. W. Begehr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with MATHEMATICS categories.
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Transmutation Operators And Applications
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Author : Vladislav V. Kravchenko
language : en
Publisher: Springer Nature
Release Date : 2020-04-11
Transmutation Operators And Applications written by Vladislav V. Kravchenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-11 with Mathematics categories.
Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.
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.
Analysis And Topology
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Author : Cabiria Andreian Cazacu
language : en
Publisher: World Scientific
Release Date : 1998-11-06
Analysis And Topology written by Cabiria Andreian Cazacu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-06 with Mathematics categories.
The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow.
Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations
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Author : A S A Mshimba
language : en
Publisher: World Scientific
Release Date : 1995-10-17
Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations written by A S A Mshimba and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-17 with categories.
These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.
Calculus Revisited
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Author : R.W. Carroll
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Calculus Revisited written by R.W. Carroll 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 2013-03-09 with Mathematics categories.
In this book the details of many calculations are provided for access to work in quantum groups, algebraic differential calculus, noncommutative geometry, fuzzy physics, discrete geometry, gauge theory, quantum integrable systems, braiding, finite topological spaces, some aspects of geometry and quantum mechanics and gravity.
Partial Differential And Integral Equations
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Author : Heinrich Begehr
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Partial Differential And Integral Equations written by Heinrich Begehr 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 2013-12-01 with Mathematics categories.
This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.