A note on the removability of totally disconnected sets for analytic functions

  • A. V. Pokrovskii

Abstract

UDC 517.537.38

We prove that each totally disconnected closed subset $E$ of a domain $G$ in the complex plane is removable for analytic functions $f(z)$ defined in $G\setminus E$ and such that for any point $z_0\in E$ the real or imaginary part of $f(z)$ vanishes at $z_0$.

 

References

W. Fedoroff,́ Sur la continuite des functions analytiques’,́ Math. Sb., 32, No 1, 115 – 121 (1924).

Ishchanov, B. Zh. On a theorem of V. S. Fedorov. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1981, no. 3, 34--37, 81. MR0641211

Ishchanov, B. Zh. A generalization of V. S. Fedorov's theorem for harmonic functions of several variables. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1986, no. 2, 100--102. MR0839427

Ishchanov, B. Zh. Extension of V. S. Fedorov's theorem to $M$-harmonic functions. (Russian) ; translated from Mat. Zametki 56 (1994), no. 5, 50--56, 158 Math. Notes 56 (1994), no. 5-6, 1132--1136 (1995) doi: 10.1007/BF02274661

Published
28.03.2020
How to Cite
PokrovskiiA. V. “A Note on the Removability of Totally Disconnected Sets for Analytic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 3, Mar. 2020, pp. 425-6, doi:10.37863/umzh.v72i3.6046.
Section
Short communications