An analogue of Hartogs lemma for separately harmonic functions with variable radius of harmonicity
S. A. ImomkulovNational University of Uzbekistan, Tashkent, UzbekistanSultanbay AbdikadirovKarakalpak State University, Nukus, Uzbekistan
ABI
Abstract
In this note we prove that if a function u(x,y) is separately harmonic in a domain D × Vr = 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.
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