Applied Pseudoanalytic Function Theory

• Κύριος συγγραφέας: Kravchenko, Vladislav V. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2009.
• Σειρά: Frontiers in Mathematics,
• Θέματα: Mathematics.; Functions of complex variables.; Operator theory.; Partial differential equations.; Physics.; Partial Differential Equations.; Mathematical Methods in Physics.; Operator Theory.; Functions of a Complex Variable.; Several Complex Variables and Analytic Spaces.

Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical...

Πίνακας περιεχομένων:

• 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.