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Generalized Analytic Functions

  • Friedrich Sauvigny
Part of the Universitext book series (UTX)

Abstract

The theory of analytic functions in one and several complex variables has been founded by Cauchy, Riemann and Weierstraß and belongs to the most beautiful mathematical creations of modern times. We recommend the textbooks of Behnke-Sommer (1955), Grauert-Fritzsche (1964, 1974), Hurwitz-Courant (1964) and Vekua (1963). The investigations of analytic functions with respect to their differentiable properties will be founded on the integral theorems from Chapter 1 and with respect to their topological properties will be based on the winding number from Chapter 3. We additionally obtain a direct approach to the solutions of the inhomogeneous Cauchy-Riemann differential equations in this chapter. In the last section we investigate the discontinuous behavior of Cauchy’s integral across the boundary.

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References

  1. [BS]
    H. Behnke, F. Sommer: Theorie der analytischen Funktionen einer komplexen Veränderlichen. Grundlehren der math. Wissenschaften 77, Springer-Verlag, Berlin …, 1955. Google Scholar
  2. [Gr]
    H. Grauert: Funktionentheorie I. Vorlesungsskriptum an der Georg-August-Universität Göttingen im Wintersemester 1964/65. Google Scholar
  3. [GF]
    H. Grauert, K. Fritzsche: Einführung in die Funktionentheorie mehrerer Veränderlicher. Hochschultext, Springer-Verlag, Berlin …, 1974. Google Scholar
  4. [HC]
    A. Hurwitz, R. Courant: Funktionentheorie. Grundlehren der math. Wissenschaften 3, 4. Auflage, Springer-Verlag, Berlin …, 1964. Google Scholar
  5. [V]
    I. N. Vekua: Verallgemeinerte analytische Funktionen. Akademie-Verlag, Berlin, 1963. Google Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Friedrich Sauvigny
    • 1
  1. 1.Mathematical Institute, LS AnalysisBrandenburgian Technical UniversityCottbusGermany

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