ガロア第一論文と乗数イデアル他関連資料スレ4

ガロア第一論文と乗数イデアル他関連資料スレ4at MATH

ガロア第一論文と乗数イデアル他関連資料スレ4 - 暇つぶし2ch187:ublication/225621333_A_generalization_of_the_Looman-Menchoff_theorem A generalization of the Looman-Menchoff theorem February 1990Israel Journal of Mathematics 70(1):93-103 DOI:10.1007/BF02807221 Authors: Venkateswara N Rao University of Toledo Download full-text PDF Citations (1) References (18) 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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