© 2009

Applied Pseudoanalytic Function Theory


  • First presentation in book of pseudoanalytic function theory applied to a variety of models of mathematical physics

  • Presents new methods for studying models of mathematical physics

  • Clearly written, at the level of an undergraduate student acquainted with complex analysis and basics of differential equations


Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. Pages 1-5
  3. Pseudoanalytic Function Theory and Second-order Elliptic Equations

  4. Applications to Sturm-Liouville Theory

  5. Applications to Real First-order Systems

    1. Front Matter
      Pages 101-101
    2. Pages 103-109
  6. Hyperbolic Pseudoanalytic Functions

  7. Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications

    1. Front Matter
      Pages 147-147
    2. Pages 149-162

About this book


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 physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods.

The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations.

It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.


Dirac equation Function theory Klein-Gordon equation Riccati equation Schrödinger equation Sturm-Liouville theory analytic function elliptic equation mathematical physics ordinary differential equation pseudoanalytic function

Authors and affiliations

  1. 1.Departamento de MatemáticasCINVESTAV del IPN Unidad Querétaro Libramiento Norponiente # 2000 Fraccionamiento Real de JuriquillaSantiago de QuerétaroMéxico

Bibliographic information

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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)