First Order Elliptic Systems
A Function Theoretic Approach
Published on 14. May 2014
295 pages
978-0-08-095669-5 (ISBN)
Description
First Order Elliptic Systems: A Function Theoretic Approach
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095669-5 (9780080956695)
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Book
01/1983
Academic Press
€60.66
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Content
- Front Cover
- First Order Elliptic Systems: A Function Theoretic Approach
- Copyright Page
- Contents
- Preface
- Chapter 0. Introduction
- Chapter 1. Elliptic Systems in the Plane
- 1. Introduction
- 2. Hyperanalytic Functions
- 3. Generalized Derivatives and the Hypercomplex Pompieu Operator
- 4. Generalized Hyperanalytic Functions and Liouville's Theorem
- 5. Cauchy Representation for Generalized Hyperanalytic Functions
- 6. M-Analytic Functions
- 7. Approximate Solutions
- Chapter 2. Boundary Value Problems
- 1. Introduction
- 2. The Plemlj Formulas
- 3. The Hilbert Problem for Hyperanalytic Functions
- 4. The Representation of a Piecewise Generalized Hyperanalytic Function in Terms of a Density
- 5. The Hilbert Problem for Generalized Hyperanalytic Functions
- 6. The Hilbert Problem in the Purely Hypercomplex Case
- 7. The Riemann-Hilbert Problem for Hypercomplex Functions
- 8. The Representation of a Generalized Hyperanalyiic Function in Terms of a Real Density
- 9. The Riemann-Hilbert Problem for Generalized Hyperanalytic Functions
- 10. The Riemann-Hilbert Problem in the Purely Hypercomplex Case
- Chapter 3. Reductions to Hyperanalyticity
- 1. Introduction
- 2. Similarity Principles
- 3. Global Similarity Principle
- 4. The Riemann-Hilbert Problem
- 5. Hyperanalytic Functions Having Distributional Boundary Data
- 6. Nonlinear Problems and Reductions to Linear Problems
- 7. Liouville's Theorem and the Similarity Principle for Pascali Systems
- Chapter 4. Function Theory over Clifford Algebras
- 1. Introduction
- 2. Regular Functions
- 3. Hilbert Modules
- 4. Liouville's Theorem
- 5. a-Holomorphic Functions
- 6. Generalized Regular Functions in Rn
- 7. Overdetermined Elliptic Systems
- 8. Function Theory for Higher Order Elliptic Systems with Analytic Coefficients
- 9. Commutative Alternatives for Higher Dimensional Function Theory
- Chapter 5. Partial Differential Equations of Several Complex Variables
- 1. Inhomogeneous Cauchy-Riemann Equations in Polycylinders
- 2. Inhomogeneous Cauchy-Riemann Systems for Several Unknowns
- 3. Existence Theorems for Solutions of Partial Differential Equations in Several Complex Variables
- 4. Real-Linear Equations in Two Complex Variables
- 5. Nonhomogeneous Cauchy-Riemann Equations in Analytic Polyhedra
- 6 . Pluriharmonic Functions
- Bibliography
- Index
