Rado's theorem for factorisations of the Laplace operator
type: Item
instance of: scholarly article
title: Rado's theorem for factorisations of the Laplace operator
zbMATH Open document ID: 1292.31001
author: E. S. Zeron
author: Carlos González-Flores
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2013-06-12T00:00:00Z
review text: Let \(\widehat{D}\) and \(D\) be a pair of first order differential operators with constant coefficients such that the product \(\widehat{D} D\) is equal to the Laplace operator. A classical theorem of Tibor Radó states that if a function \(h\) is continuous on an open set \(\Omega\subset \mathbb{C}^n\) and holomorphic on the complement of its zero locus, then it is holomorphic everywhere on \(\Omega\). This paper extends this classical result by substituting the holomorphicity of \(h\) with the assumptions that \(Dh\) vanishes.
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6174721
zbMATH Keywords: Laplace operator
zbMATH Keywords: Radó's theorem for holomorphic functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6174721