Yoshihiro Sawano'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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464

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Springer

Published Date

ISBN 10

9811005303

ISBN 13

9789811005305

Morrey Spaces

Introduction and Applications to Integral Operators and PDE’s, Volumes I & II

By: Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim

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Morrey Spaces

Introduction and Applications to Integral Operators and PDE’s, Volumes I & II

By: Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with focus on harmonic analysis in volume I and generalizations and interpolation of Morrey spaces in volume II. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

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Page Count

386

Publisher

CRC Press

Published Date

ISBN 10

1000064131

ISBN 13

9781000064131

Theory of Besov Spaces

By: Yoshihiro Sawano

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Theory of Besov Spaces

By: Yoshihiro Sawano

This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

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964

Publisher

Springer

Published Date

ISBN 10

9811308365

ISBN 13

9789811308369

Theory of Besov Spaces

By: Yoshihiro Sawano

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Theory of Besov Spaces

By: Yoshihiro Sawano

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Page Count

964

Publisher

Springer

Published Date

ISBN 10

9811308365

ISBN 13

9789811308369

Morrey Spaces

Introduction and Applications to Integral Operators and PDE’s, Volume I

By: Yoshihiro Sawano

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Morrey Spaces

Introduction and Applications to Integral Operators and PDE’s, Volume I

By: Yoshihiro Sawano

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

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Page Count

386

Publisher

CRC Press

Published Date

ISBN 10

0429532024

ISBN 13

9780429532023

Morrey Spaces

Introduction and Applications to Integral Operators and PDE’s, Volume II

By: Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim

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Morrey Spaces

Introduction and Applications to Integral Operators and PDE’s, Volume II

By: Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim

Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

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Page Count

429

Publisher

CRC Press

Published Date

ISBN 10

1000064050

ISBN 13

9781000064056

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

Book's by Yoshihiro Sawano

Theory of Reproducing Kernels and Applications

Theory of Reproducing Kernels and Applications

Morrey Spaces

Morrey Spaces

Theory of Besov Spaces

Theory of Besov Spaces

Theory of Besov Spaces

Theory of Besov Spaces

Morrey Spaces

Morrey Spaces

Morrey Spaces

Morrey Spaces

Theory of Reproducing Kernels and Applications

Theory of Reproducing Kernels and Applications

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