A simple proof of the Radó and Král theorems on removability of the zero locus for analytic and harmonic functions

A.V. Pokrovskii

doi:10.15407/dopovidi2015.07.029

A simple proof of the Radó and Král theorems on removability of the zero locus for analytic and harmonic functions

Authors

A.V. Pokrovskii

DOI:

https://doi.org/10.15407/dopovidi2015.07.029

Keywords:

analytic function, harmonic function, Radó theorem, subharmonic function, zero locus

Abstract

A unified approach to the proof of the Radó and Král theorems on removability of the zero locus for analytic and harmonic functions is proposed.

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References

Radó T. Math. Z., 1924, 20: 1–6. https://doi.org/10.1007/BF01188068

Král J. J. London Math. Soc., 1983, 28, No 1: 62–70. https://doi.org/10.1112/jlms/s2-28.1.62

Rudin W. Real and complex analysis, New York; London: McGraw-Hill, 1987.

Stout E. L. Polynomial convexity, Boston, MA: Birkhäuser, 2007.

Harvey R., Polking J.C. Acta Math., 1970, 125, No 1-2: 39–56. https://doi.org/10.1007/BF02838327

Juutinen P., Lindqvist P. Commun. Part. Diff. Eq., 2005, 30, No 3: 305–321. https://doi.org/10.1081/PDE-200050030

Stein E.M., Weiss G. Acta Math., 1960, 103, No 1-2: 25–62. https://doi.org/10.1007/BF02546524

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Published

05.02.2025

How to Cite

Pokrovskii, A. (2025). A simple proof of the Radó and Král theorems on removability of the zero locus for analytic and harmonic functions . Reports of the National Academy of Sciences of Ukraine, (7), 29–31. https://doi.org/10.15407/dopovidi2015.07.029