Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂn

Mark L. Agranovsky

doi:10.1007/s11854-011-0008-9

Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂⁿ

Mark L. Agranovsky

Department of Mathematics

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

21 Scopus citations

Abstract

Let f ∈ C^ω(∂Bⁿ), where Bⁿ is the unit ball of ℂⁿ. We prove that if a,b ∈ B̄ⁿ, a ≠ b, for every complex line L passing through one of a or b, the restricted function f{pipe}L∩∂Bⁿ has a holomorphic extention to the cross-section L∩Bⁿ, then f is the boundary value of a holomorphic function in Bⁿ.

Original language	English
Pages (from-to)	293-304
Number of pages	12
Journal	Journal d'Analyse Mathematique
Volume	113
Issue number	1
DOIs	https://doi.org/10.1007/s11854-011-0008-9
State	Published - Jan 2011

Bibliographical note

Funding Information:
∗This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.

Funding

∗This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.

Funders	Funder number
Israel Science Foundation	688/08

Access to Document

10.1007/s11854-011-0008-9

Cite this

@article{d0fbe9e029994e229edd3cfd577dcb3d,

title = "Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂn",

abstract = "Let f ∈ Cω(∂Bn), where Bn is the unit ball of ℂn. We prove that if a,b ∈ {\=B}n, a ≠ b, for every complex line L passing through one of a or b, the restricted function f{pipe}L∩∂Bn has a holomorphic extention to the cross-section L∩Bn, then f is the boundary value of a holomorphic function in Bn.",

author = "Agranovsky, {Mark L.}",

note = "Funding Information: ∗This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.",

year = "2011",

month = jan,

doi = "10.1007/s11854-011-0008-9",

language = "אנגלית",

volume = "113",

pages = "293--304",

journal = "Journal d'Analyse Mathematique",

issn = "0021-7670",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂn

AU - Agranovsky, Mark L.

N1 - Funding Information: ∗This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.

PY - 2011/1

Y1 - 2011/1

N2 - Let f ∈ Cω(∂Bn), where Bn is the unit ball of ℂn. We prove that if a,b ∈ B̄n, a ≠ b, for every complex line L passing through one of a or b, the restricted function f{pipe}L∩∂Bn has a holomorphic extention to the cross-section L∩Bn, then f is the boundary value of a holomorphic function in Bn.

AB - Let f ∈ Cω(∂Bn), where Bn is the unit ball of ℂn. We prove that if a,b ∈ B̄n, a ≠ b, for every complex line L passing through one of a or b, the restricted function f{pipe}L∩∂Bn has a holomorphic extention to the cross-section L∩Bn, then f is the boundary value of a holomorphic function in Bn.

UR - http://www.scopus.com/inward/record.url?scp=79954986274&partnerID=8YFLogxK

U2 - 10.1007/s11854-011-0008-9

DO - 10.1007/s11854-011-0008-9

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:79954986274

SN - 0021-7670

VL - 113

SP - 293

EP - 304

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

IS - 1

ER -