Transformations, Transmutations, and Kernel Functions PDF Download
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Author: H Begehr
Publisher: CRC Press
ISBN: 9780582091092
Category : Mathematics
Languages : en
Pages : 286
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Book Description
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.
Author: H Begehr
Publisher: CRC Press
ISBN: 9780582091092
Category : Mathematics
Languages : en
Pages : 286
Get Book Here
Book Description
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.
Author: H Begehr
Publisher: CRC Press
ISBN: 100094655X
Category : Mathematics
Languages : en
Pages : 280
Get Book Here
Book Description
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.
Author: H Begehr
Publisher: CRC Press
ISBN: 1000951510
Category : Mathematics
Languages : en
Pages : 286
Get Book Here
Book Description
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.
Author: Heinrich G. W. Begehr
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 0
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Book Description
Author: Heinrich G. W. Begehr
Publisher: Chapman and Hall/CRC
ISBN:
Category : Mathematics
Languages : en
Pages : 424
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Book Description
A broad ranging collection of recent results in the subject covering areas from plane elasticity to second and higher order elliptic equations. The chapters may be read individually, providing a more accessible forum for the applications.
Author: Heinrich G. W. Begehr
Publisher:
ISBN: 9781003417019
Category : MATHEMATICS
Languages : en
Pages : 0
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Book Description
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.
Author: H Begehr
Publisher: Chapman and Hall/CRC
ISBN: 9780582091092
Category : Mathematics
Languages : en
Pages : 280
Get Book Here
Book Description
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.
Author: Saburou Saitoh
Publisher: CRC Press
ISBN: 1000115240
Category : Mathematics
Languages : en
Pages : 289
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Book Description
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: Vladislav V. Kravchenko
Publisher: Springer Nature
ISBN: 303035914X
Category : Mathematics
Languages : en
Pages : 685
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Book Description
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.
Author: Saburou Saitoh
Publisher: Springer
ISBN: 9811005303
Category : Mathematics
Languages : en
Pages : 464
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Book Description
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.
