Applied Pseudoanalytic Function Theory
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 re
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Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) Benoît Perthame (Université Pierre et Marie Curie, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (Macquarie University, New South Wales) Wolfgang Sprössig (TU Bergakademie Freiberg) Cédric Vilani (Ecole Normale Supérieure, Lyon)
Vladislav V. Kravchenko
Applied
Pseudoanalytic
Function
Theory
Birkhäuser Verlag Basel . Boston . Berlin
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Contents
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Part I Pseudoanalytic Function Theory and Second-order Elliptic Equations 2 Definitions and Results from Bers’ Theory 2.1 Generating pairs and differentiation . . . . . . . . . . 2.2 Pseudoanalytic functions . . . . . . . . . . . . . . . . 2.3 Derivatives and integrals of pseudoanalytic functions 2.3.1 Equivalent generating pairs . . . . . . . . . . 2.3.2 Vekua’s equation for (F, G)-derivatives . . . . 2.3.3 Integration . . . . . . . . . . . . . . . . . . .
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3 Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions 3.1 Factorization of the stationary Schr¨ odinger operator . . . . 3.2 Factorization of the operator div p grad +q. . . . . . . . . . 3.3 Conjugate metaharmonic functions . . . . . . . . . . . . . . 3.4 The main Vekua equation
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