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A pure smoothness condition for radó’s theorem for α-analytic functions

Daghighi, Abtin and Wikström, Frank LU (2016) In Czechoslovak Mathematical Journal 66(1). p.57-62
Abstract

Let (Formula presented.) be a bounded, simply connected ℂ-convex domain. Let α ∈ ℤ+ n and let f be a function on Ω which is separately (Formula presented.) -smooth with respect to zj (by which we mean jointly (Formula presented.) -smooth with respect to Rezj, Imzj). If f is α-analytic on Ω\f−1(0), then f is α-analytic on Ω. The result is well-known for the case αi = 1, 1 ⩽ i ⩽ n, even when f a priori is only known to be continuous.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
polyanalytic function, Radó’s theorem, zero set, α-analytic function
in
Czechoslovak Mathematical Journal
volume
66
issue
1
pages
6 pages
publisher
Springer New York
external identifiers
  • Scopus:84962850799
ISSN
0011-4642
DOI
10.1007/s10587-016-0238-1
language
English
LU publication?
yes
id
30be643c-65e5-499c-b1ac-fa2424bd728f
date added to LUP
2016-07-14 12:34:51
date last changed
2016-07-14 12:34:51
@misc{30be643c-65e5-499c-b1ac-fa2424bd728f,
  abstract     = {<p>Let (Formula presented.) be a bounded, simply connected ℂ-convex domain. Let α ∈ ℤ<sub>+</sub>         <sup>n</sup> and let f be a function on Ω which is separately (Formula presented.) -smooth with respect to z<sub>j</sub> (by which we mean jointly (Formula presented.) -smooth with respect to Rez<sub>j</sub>, Imz<sub>j</sub>). If f is α-analytic on Ω\f<sup>−1</sup>(0), then f is α-analytic on Ω. The result is well-known for the case α<sub>i</sub> = 1, 1 ⩽ i ⩽ n, even when f a priori is only known to be continuous.</p>},
  author       = {Daghighi, Abtin and Wikström, Frank},
  issn         = {0011-4642},
  keyword      = {polyanalytic function,Radó’s theorem,zero set,α-analytic function},
  language     = {eng},
  month        = {03},
  number       = {1},
  pages        = {57--62},
  publisher    = {ARRAY(0x843c438)},
  series       = {Czechoslovak Mathematical Journal},
  title        = {A pure smoothness condition for radó’s theorem for α-analytic functions},
  url          = {http://dx.doi.org/10.1007/s10587-016-0238-1},
  volume       = {66},
  year         = {2016},
}