A. Logunov

activity

20132026

most citedOn ratios of harmonic functions

15 citations · 47 across the 16 of their papers we have counts for

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Showing 2014 · math.APShow all

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math.AP2014

On the higher-dimensional harmonic analog of the Levinson log log theorem

Alexander Logunov

Let $M : (0, 1) \to [e, + \infty)$ be a decreasing function such that $0 \int 1 lo g lo g M (y) d y < + \infty$ . Consider the set $H_{M}$ of all functions $u$ harmonic in $P:=\{(…

math.AP2014★ 15 cited

On ratios of harmonic functions

Alexander Logunov, Eugenia Malinnikova

Let $u$ and $v$ be harmonic in $Ω \subset R^{n}$ functions with the same zero set $Z$ . We show that the ratio $f$ of such functions is always well-defined and is real analyt…