Theory of Reproducing Kernels and Applications
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The work Theory of Reproducing Kernels and Applications represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Theory of Reproducing Kernels and Applications
Resource Information
The work Theory of Reproducing Kernels and Applications represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Theory of Reproducing Kernels and Applications
 Statement of responsibility
 by Saburou Saitoh, Yoshihiro Sawano
 Subject

 Functions of a Complex Variable
 Functional analysis
 Fourier analysis
 Partial differential equations
 Partial differential equations
 Functional Analysis
 Electronic resources
 Fourier Analysis
 Functional Analysis
 Functions of complex variables
 Fourier analysis
 Mathematics
 Functions of complex variables
 Mathematics
 Fourier Analysis
 Partial Differential Equations
 Functional analysis
 Partial Differential Equations
 Language
 eng
 Summary
 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 selfcontained 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 eigenfunctions, 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, and as 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
 Image bit depth
 0
 LC call number
 QA319329.9
 Literary form
 non fiction
 Series statement
 Developments in Mathematics,
 Series volume
 44
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