Israel Journal of Mathematics

, Volume 70, Issue 1, pp 93–103

A generalization of the Looman-Menchoff theorem

  • N. V. Rao
Article
  • 72 Downloads

Abstract

In this paper we give a generalization of the classical Looman-Menchoff theorem:If f is a complex-valued continuous function of a complex variable in a domain G, f has partial derivatives fxand fyeverywhere in G and the Cauchy Riemann equations fx +ify = 0are satisfied almost everywhere, then f is holomorphic in G. From our generalization of this theorem, we deduce a theroem of Sindalovskii [9] as a corollary and also answer some of the questions raised in [9]. We note in this context that, as far as we know, Sindalovskii’s result is the best published to date in this area.

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Copyright information

© Hebrew University 1990

Authors and Affiliations

  • N. V. Rao
    • 1
  1. 1.Department of MathematicsUniversity of ToledoToledoUSA

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