TY - JOUR
T1 - Hartogs extension for generalized tubes in Cn
AU - Boggess, Albert
AU - Dwilewicz, R. J.
AU - Slodkowski, Z.
N1 - Funding Information:
The second author was partially supported by the Missouri Research Board grant 2011–2013.
PY - 2013/6/15
Y1 - 2013/6/15
N2 - In 1906, Hartogs proved his famous holomorphic extension theorem for bounded domains in Cn, however, not many results of this type exist for unbounded ones. One of such, already a classical result, is the Bochner tube theorem from 1938, and in this paper we consider its generalization to "widening tubes". Namely, we establish a sufficient condition for holomorphic extension of CR functions from the boundary of a certain class of domains in Cn, n≥ 2, which possess a growth condition at infinity.
AB - In 1906, Hartogs proved his famous holomorphic extension theorem for bounded domains in Cn, however, not many results of this type exist for unbounded ones. One of such, already a classical result, is the Bochner tube theorem from 1938, and in this paper we consider its generalization to "widening tubes". Namely, we establish a sufficient condition for holomorphic extension of CR functions from the boundary of a certain class of domains in Cn, n≥ 2, which possess a growth condition at infinity.
KW - CR functions
KW - Hartogs-type extension
KW - Holomorphic functions
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U2 - 10.1016/j.jmaa.2013.01.049
DO - 10.1016/j.jmaa.2013.01.049
M3 - Article
AN - SCOPUS:84875376133
SN - 0022-247X
VL - 402
SP - 574
EP - 578
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -