Israel Journal of Mathematics

, Volume 70, Issue 1, pp 93–103

A generalization of the Looman-Menchoff theorem

Authors

  • N. V. Rao
    • Department of MathematicsUniversity of Toledo
Article

DOI: 10.1007/BF02807221

Cite this article as:
Rao, N.V. Israel J. Math. (1990) 70: 93. doi:10.1007/BF02807221

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 f x and f y everywhere in G and the Cauchy Riemann equations f x +if y = 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.

Copyright information

© Hebrew University 1990