Abels Pseudodifferential and Singular Integral Operators

An Introduction with Applications
1. Auflage 2011
ISBN: 978-3-11-025031-2
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 232 Seiten

Reihe: De Gruyter Textbook

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations.

In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix.

The text is comprehensible for students of mathematics and physics with a basic education in analysis.

Zielgruppe

Students and Lecturers in Mathematics and Physics; Academic Libraries

Autoren/Hrsg.

Abels, Helmut

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Frontmatter

Preface

Contents

Chapter. 1 Introduction

Part I. Fourier Transformation and Pseudodifferential Operators Chapter 2. Fourier Transformation and Tempered Distributions Chapter 3. Basic Calculus of Pseudodifferential Operators on Rn

Part II. Singular Integral Operators Chapter 4. Translation Invariant Singular Integral Operators Chapter 5. Non-Translation Invariant Singular Integral Operators

Part III. Applications to Function Space and Differential Equations Chapter 6. Introduction to Besov and Bessel Potential Spaces Chapter 7. Applications to Elliptic and Parabolic Equations

Part IV. Appendix Appendix A Basic Results from Analysis

Bibliography

Index

Über Autor(innen)

Abels, Helmut
Helmut Abels, University of Regensburg, Germany.