Continuation of separately analytic functions defined on part of a domain boundary

Autor:	S. A. Imomkulov, A. S. Sadullaev
Rok vydání:	2006
Předmět:	Discrete mathematics Plurisubharmonic function Lebesgue measure General Mathematics Analytic continuation Holomorphic function Boundary (topology) Hartogs' theorem Pluripolar set Domain (mathematical analysis) Mathematics
Zdroj:	Mathematical Notes. 79:869-877
ISSN:	1573-8876 0001-4346
DOI:	10.1007/s11006-006-0098-3
Popis:	Let D ⊂ ℂn be a domain with smooth boundary ∂D, let E⊂∂D be a subset of positive Lebesgue measure mes(E) > 0, and let F ⊂ G be a nonpluripolar compact set in a strongly pseudoconvex domain D ⊂ ℂm. We prove that, under an additional condition, each function separately analytic on the set X = (D × F) ∪ (E × G) has a holomorphic contination to the domain \(\rlap{--} X = \{ (z,w) \in D \times G:\omega _{in}^ * (z,E,D) + \omega ^ * (w,F,D) < 1\} \), where ω* is the P-measure and ω*in is the interior P-measure.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9b814662746836cfb771270febef4a4e https://doi.org/10.1007/s11006-006-0098-3 Zobrazit plný text záznamu Plný text ve formátu PDF