Boundary cross theorem in dimension 1

Peter Pflug, and Viêt-Anh Nguyên. "Boundary cross theorem in dimension 1." Annales Polonici Mathematici 90.2 (2007): 149-192. <http://eudml.org/doc/280271>.

@article{PeterPflug2007,
abstract = {Let X, Y be two complex manifolds of dimension 1 which are countable at infinity, let D ⊂ X, G ⊂ Y be two open sets, let A (resp. B) be a subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B) ∪ (A×(B∪G)). Suppose in addition that D (resp. G) is Jordan-curve-like on A (resp. B) and that A and B are of positive length. We determine the "envelope of holomorphy" Ŵ of W in the sense that any function locally bounded on W, measurable on A × B, and separately holomorphic on (A × G) ∪ (D × B) "extends" to a function holomorphic on the interior of Ŵ.},
author = {Peter Pflug, Viêt-Anh Nguyên},
journal = {Annales Polonici Mathematici},
keywords = {boundary cross theorem; Carleman formula; Gonchar-Carleman operator; holomorphic extension; harmonic measure},
language = {eng},
number = {2},
pages = {149-192},
title = {Boundary cross theorem in dimension 1},
url = {http://eudml.org/doc/280271},
volume = {90},
year = {2007},
}

TY - JOUR
AU - Peter Pflug
AU - Viêt-Anh Nguyên
TI - Boundary cross theorem in dimension 1
JO - Annales Polonici Mathematici
PY - 2007
VL - 90
IS - 2
SP - 149
EP - 192
AB - Let X, Y be two complex manifolds of dimension 1 which are countable at infinity, let D ⊂ X, G ⊂ Y be two open sets, let A (resp. B) be a subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B) ∪ (A×(B∪G)). Suppose in addition that D (resp. G) is Jordan-curve-like on A (resp. B) and that A and B are of positive length. We determine the "envelope of holomorphy" Ŵ of W in the sense that any function locally bounded on W, measurable on A × B, and separately holomorphic on (A × G) ∪ (D × B) "extends" to a function holomorphic on the interior of Ŵ.
LA - eng
KW - boundary cross theorem; Carleman formula; Gonchar-Carleman operator; holomorphic extension; harmonic measure
UR - http://eudml.org/doc/280271
ER -