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

Daghighi, Abtin and Wikström, Frank LU orcid (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.

Please use this url to cite or link to this publication:
author
and
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
external identifiers
  • scopus:84962850799
  • wos:000373671300006
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
2025-01-12 08:55:04
@article{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}},
  keywords     = {{polyanalytic function; Radó’s theorem; zero set; α-analytic function}},
  language     = {{eng}},
  month        = {{03}},
  number       = {{1}},
  pages        = {{57--62}},
  publisher    = {{Springer}},
  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}},
  doi          = {{10.1007/s10587-016-0238-1}},
  volume       = {{66}},
  year         = {{2016}},
}