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Applied Pseudoanalytic Function Theory

  • Vladislav V. Kravchenko

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

  8. Back Matter
    Pages 171-184

About this book

Introduction

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.

Keywords

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

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

Bibliographic information