Applied Pseudoanalytic Function Theory

• Pseudoanalytic Function Theory and Second-order Elliptic Equations.- Definitions and Results from Bers’ Theory.- Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions.- Formal Powers.- Cauchy’s Integral Formula.- Complex Riccati Equation.- Applications to Sturm-Liouville Theory.- A Representation for Solutions of the Sturm-Liouville Equation.- Spectral Problems and Darboux Transformation.- Applications to Real First-order Systems.- Beltrami Fields.- Static Maxwell System in Axially Symmetric Inhomogeneous Media.- Hyperbolic Pseudoanalytic Functions.- Hyperbolic Numbers and Analytic Functions.- Hyperbolic Pseudoanalytic Functions.- Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation.- Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications.- The Dirac Equation.- Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions.- Multidimensional Second-order Equations.

From the reviews: "This book presents a renaissance of Bers' and Vekua's theory. It can be recommended to colleagues which are interested in the plane function theory." (Michael Reissig, Zentralblatt MATH, Vol. 1182, 2010)