Theory of Reproducing Kernels and Applications (Developments in Mathematics Book 44) By Saburou Saitoh Kindle Edition 9811005303 9789811005305 Theory of Reproducing Kernels and Applications (Developments in Mathematics Book 44) 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, Yamadas unified and generalized inequalities for Opials inequalities and the concrete and explicit integral representation of the implicit functions are presented.
EPub Theory of Reproducing Kernels and 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.
EPub Theory of Reproducing Kernels and applications folder 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.
Theory of reproducing kernels and applications pdf free 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.
Theory of Reproducing Kernels and Applications kindle store 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.
Theory of reproducing kernels and applicationsbook 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 Theory of Reproducing Kernels and Applications Developments in Mathematics Book 44
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Book Theory of Reproducing Kernels and applications folder
This book provides a large extension of the general theory of reproducing kernels published by N Aronszajn in 1950 with many concrete applications.
Book theory of reproducing kernels and applications pdf free download 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