Hartogs extension for generalized tubes in Cn

Albert Boggess; R. J. Dwilewicz; Z. Slodkowski

doi:10.1016/j.jmaa.2013.01.049

Hartogs extension for generalized tubes in Cn

Albert Boggess
, R. J. Dwilewicz
, Z. Slodkowski

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	574-578
Number of pages	5
Journal	Journal of Mathematical Analysis and Applications
Volume	402
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2013.01.049
State	Published - Jun 15 2013

Keywords

CR functions
Hartogs-type extension
Holomorphic functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2013.01.049

Cite this

@article{6ebeacfeae5e4c5bb2bb4e7ca86c2d17,

title = "Hartogs extension for generalized tubes in Cn",

abstract = "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.",

keywords = "CR functions, Hartogs-type extension, Holomorphic functions",

author = "Albert Boggess and Dwilewicz, \{R. J.\} and Z. Slodkowski",

note = "Funding Information: The second author was partially supported by the Missouri Research Board grant 2011–2013.",

year = "2013",

month = jun,

day = "15",

doi = "10.1016/j.jmaa.2013.01.049",

language = "English (US)",

volume = "402",

pages = "574--578",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

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

UR - https://www.scopus.com/pages/publications/84875376133

UR - https://www.scopus.com/pages/publications/84875376133#tab=citedBy

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 -

Hartogs extension for generalized tubes in Cn

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this