An analogue of Hartogs lemma for separately harmonic functions with variable radius of harmonicity

Authors

Sevdiyor Imomkulov, National University of Uzbekistan, Tashkent, Uzbekistan; Institute of Mathematics named after V.I.Romanovsky, Tashkent, UzbekistanFollow
Sultanbay Abdikadirov, Institute of Mathematics named after V.I.Romanovsky, Tashkent, Uzbekistan; Karakalpak State University, Nukus, UzbekistanFollow

Abstract

In this note we prove that if a function u(x,y) is separately harmonic in a domain D × V_r = D × {y∈ℝ²:|y|<r,  r>1} ⊂ ℝⁿ × ℝ² and for each fixed point x⁰ ∈ D the function u(x⁰,y) of variable y continues harmonically into the great circle {y∈ℝ²:|y|<R(x⁰),  R(x⁰)>r}, then it continues harmonically into a domain {(x,y)∈ℝⁿ×ℝ²:|y|<R_*(x),    x∈D} over a set of variables.

First Page

214

Last Page

224

References

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Recommended Citation

Imomkulov, Sevdiyor and Abdikadirov, Sultanbay (2023) "An analogue of Hartogs lemma for separately harmonic functions with variable radius of harmonicity," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 6: Iss. 4, Article 5.
DOI: https://doi.org/10.56017/2181-1318.1262