Saburou Saitoh's Books

Theory of Reproducing Kernels and Applications

By: Saburou Saitoh,Yoshihiro Sawano

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Theory of Reproducing Kernels and Applications

By: Saburou Saitoh,Yoshihiro Sawano

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.

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Page Count

464

Publisher

Springer

Published Date

ISBN 10

9811005303

ISBN 13

9789811005305

Introduction to the Division by Zero Calculus

By: SABUROU SAITOH

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Introduction to the Division by Zero Calculus

By: SABUROU SAITOH

The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.

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Page Count

203

Publisher

Scientific Research Publishing, Inc. USA

Published Date

ISBN 10

1649970897

ISBN 13

9781649970893

Integral Transforms, Reproducing Kernels and Their Applications

By: Saburou Saitoh

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Integral Transforms, Reproducing Kernels and Their Applications

By: Saburou Saitoh

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.

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Page Count

300

Publisher

CRC Press

Published Date

ISBN 10

1000158047

ISBN 13

9781000158045

Division by Zero Calculus—History and Development

By: Saburou Saitoh

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Division by Zero Calculus—History and Development

By: Saburou Saitoh

This is based on the record of how I have been discovering and pioneering a new world by breaking the first of the Ten Commandments of Mathematics, which has been 2300 years since Aristotle and must not be divided by zero. I am involved in the basic issues of humankind involved in mathematical physics, philosophy, and worldview. What is eternity and what is infinity? What is the significance of human existence?

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Page Count

333

Publisher

Scientific Research Publishing, Inc. USA

Published Date

ISBN 10

1649972253

ISBN 13

9781649972255

Theory of Reproducing Kernels and Applications

By: Saburou Saitoh,Yoshihiro Sawano

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Theory of Reproducing Kernels and Applications

By: Saburou Saitoh,Yoshihiro Sawano

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Solve jigsaw puzzle

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Page Count

464

Publisher

Springer

Published Date

ISBN 10

9811005303

ISBN 13

9789811005305

Integral Transforms, Reproducing Kernels and Their Applications

By: Saburou Saitoh

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Integral Transforms, Reproducing Kernels and Their Applications

By: Saburou Saitoh

Average ratings

N/A

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Solve jigsaw puzzle

Age

Page Count

300

Publisher

CRC Press

Published Date

ISBN 10

1000158047

ISBN 13

9781000158045

Book's by Saburou Saitoh

Theory of Reproducing Kernels and Applications

Theory of Reproducing Kernels and Applications

Introduction to the Division by Zero Calculus

Introduction to the Division by Zero Calculus

Integral Transforms, Reproducing Kernels and Their Applications

Integral Transforms, Reproducing Kernels and Their Applications

Division by Zero Calculus—History and Development

Division by Zero Calculus—History and Development

Theory of Reproducing Kernels and Applications

Theory of Reproducing Kernels and Applications

Integral Transforms, Reproducing Kernels and Their Applications

Integral Transforms, Reproducing Kernels and Their Applications

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