First Order Elliptic Systems

Name: First Order Elliptic Systems | A Function Theoretic Approach
Brand: Academic Press
Price: 61.95 EUR
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A Function Theoretic Approach

Buchanan(Autor*in)

Buchanan(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

295 Seiten

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978-0-08-095669-5 (ISBN)

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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

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