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 Títol: On L^p-solutions to the Laplace equation and zeros of holomorphic functions Autor: Bruna, Joaquim; Ortega Cerdà, Joaquim Data: 1996 Tipus de document: Article Resum: The problem we solve in this paper is to characterize, in a smooth domain $\Omega$ in $\Bbb R^n$ and for $1\le p\le\infty$, those positive Borel measures on $\Omega$ for which there exists a subharmonic function $u\in L^p(\Omega)$ such that $\Delta u=\mu$. The motivation for this question is mainly for $n=2$, in which case it is related with problems about distributions of zeros of holomorphic functions: If $\{a_n\}^{\infty}_{n=1}$ is a sequence in $\Omega\subset\Bbb C$ with no accumulation points in a simply connected domain $\Omega$, and $\mu=2\pi\sum_n\delta_{a_n}$, then all solutions $u$ of $\Delta u=\mu$ are of the form $u=\log |f|$, with $f$ holomorphic vanishing exactly on the poits $a_n$. Thus our results give the characterization of the zero sequences of holomorphic functions with $\log |f|\in L^p(\Omega)$. A related class had been considered by Beller. URI: http://hdl.handle.net/2117/1224 Apareix a les col·leccions: Departaments de Matemàtica Aplicada. Articles de revista Comparteix: