Cross theorem

Marek Jarnicki, and Peter Pflug. "Cross theorem." Annales Polonici Mathematici 77.3 (2001): 295-302. <http://eudml.org/doc/280744>.

@article{MarekJarnicki2001,
abstract = {Let D,G ⊂ ℂ be domains, let A ⊂ D, B ⊂ G be locally regular sets, and let X:= (D×B)∪(A×G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset M̂ of the envelope of holomorphy X̂ of X such that any function separately holomorphic on X∖M extends to a holomorphic function on X̂ ∖M̂. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], and [Sic 2000].},
author = {Marek Jarnicki, Peter Pflug},
journal = {Annales Polonici Mathematici},
keywords = {separately holomorphic function; locally regular; locally pluriregular; pluriregular; cross-theorem; envelope of holomorphy},
language = {eng},
number = {3},
pages = {295-302},
title = {Cross theorem},
url = {http://eudml.org/doc/280744},
volume = {77},
year = {2001},
}

TY - JOUR
AU - Marek Jarnicki
AU - Peter Pflug
TI - Cross theorem
JO - Annales Polonici Mathematici
PY - 2001
VL - 77
IS - 3
SP - 295
EP - 302
AB - Let D,G ⊂ ℂ be domains, let A ⊂ D, B ⊂ G be locally regular sets, and let X:= (D×B)∪(A×G). Assume that A is a Borel set. Let M be a proper analytic subset of an open neighborhood of X. Then there exists a pure 1-dimensional analytic subset M̂ of the envelope of holomorphy X̂ of X such that any function separately holomorphic on X∖M extends to a holomorphic function on X̂ ∖M̂. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], and [Sic 2000].
LA - eng
KW - separately holomorphic function; locally regular; locally pluriregular; pluriregular; cross-theorem; envelope of holomorphy
UR - http://eudml.org/doc/280744
ER -