Theory of Reproducing Kernels and Applications

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Mathematical Analysis
Cover of the book Theory of Reproducing Kernels and Applications by Saburou Saitoh, Yoshihiro Sawano, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Saburou Saitoh, Yoshihiro Sawano ISBN: 9789811005305
Publisher: Springer Singapore Publication: October 14, 2016
Imprint: Springer Language: English
Author: Saburou Saitoh, Yoshihiro Sawano
ISBN: 9789811005305
Publisher: Springer Singapore
Publication: October 14, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Atlas of Ocular Trauma by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Diabetes Mellitus in 21st Century by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Learning Through School Science Investigation by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Japanese Management for a Globalized World by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Rural Labour Mobility in Times of Structural Transformation by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Therapeutic Angiogenesis by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Parts of Speech in Mandarin by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Genome Analysis and Human Health by Saburou Saitoh, Yoshihiro Sawano
Cover of the book A Post-Colonial Enquiry into Europe’s Debt and Migration Crisis by Saburou Saitoh, Yoshihiro Sawano
Cover of the book 3rd International Conference on Radiation Safety & Security in Healthcare Services by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Mathematical Insights into Advanced Computer Graphics Techniques by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Statistical Modeling for Degradation Data by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Advanced Functional Materials by Saburou Saitoh, Yoshihiro Sawano
Cover of the book Conservation Agriculture by Saburou Saitoh, Yoshihiro Sawano
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy