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

Authors

  • A. V. Pokrovskii

DOI:

https://doi.org/10.37863/umzh.v72i3.6046

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∖E and such that for any point z0∈E the real or imaginary part of f(z) vanishes at z0.

 

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

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Published

28.03.2020

Issue

Vol. 72 No. 3 (2020)

Section

Short communications

How to Cite

Pokrovskii, A. 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, https://doi.org/10.37863/umzh.v72i3.6046.