Pseudodifferential and Singular Integral Operators : : An Introduction with Applications / / Helmut Abels.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Abels, Helmut,
• MitwirkendeR: Abels, Helmut,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2012
• Year of Publication: 2011
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (222 p.)

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.

Table of Contents

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