A generalization of the Looman-Menchoff theorem |
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Authors: | N. V. Rao |
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Affiliation: | (1) Department of Mathematics, University of Toledo, 43606 Toledo, OH, USA |
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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. |
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