Generators of the algebra of holomorphic functions with log-type growth

• Autores: Michal Jasiczak
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 2, 2008, págs. 545-564
• Idioma: inglés
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• Resumen

  • In this paper we address the problem of solvability of the Bézout equation in the algebra of holomorphic functions, which grow not faster than some power of logarithm of the distance to the boundary. It is proved that if the domain is smoothly bounded and strongly pseudoconvex then two such functions generate the algebra, if they are jointly invertible in the corresponding algebra of continuous functions. The method relies on explicit formulae for the Neumann operator given by Lieb and Range. As a result, we also obtain some regularity results for the Neumann operator.