Applied Pseudoanalytic Function Theory

1. Introduction

Part I. Pseudoanalytic Function Theory and Second-order Elliptic Equations

2. Definitions and Results from Bers’ Theory

3. Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions

4. Formal Powers

5. Cauchy’s Integral Formula

6. Complex Riccati Equation

Part II. Applications to Sturm-Liouville Theory

7. A Representation for Solutions of the Sturm-Liouville Equation

8. Spectral Problems and Darboux Transformation

Part III. Applications to Real First-order Systems

9. Beltrami Fields

10. Static Maxwell System in Axially Symmetric Inhomogeneous Media

Part IV. Hyperbolic Pseudoanalytic Functions

11. Hyperbolic Numbers and Analytic Functions

12. Hyperbolic Pseudoanalytic Functions

13. Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation

Part V. Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications

14. The Dirac Equation

15. Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions

16. Multidimensional Second-order Equations

Keywords: Mathematics, Partial Differential Equations, Mathematical Methods in Physics, Operator Theory, Functions of a Complex Variable, Several Complex Variables and Analytic Spaces