A pure smoothness condition for Radó’s theorem for αanalytic functions
(2016) In Czechoslovak Mathematical Journal 66(1). p.5762 Abstract
Let (Formula presented.) be a bounded, simply connected ℂconvex domain. Let α ∈ ℤ_{+} ^{n} and let f be a function on Ω which is separately (Formula presented.) smooth with respect to z_{j} (by which we mean jointly (Formula presented.) smooth with respect to Rez_{j}, Imz_{j}). If f is αanalytic on Ω\f^{−1}(0), then f is αanalytic on Ω. The result is wellknown for the case α_{i} = 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:
http://lup.lub.lu.se/record/30be643c65e5499cb1acfa2424bd728f
 author
 Daghighi, Abtin and Wikström, Frank ^{LU}
 organization
 publishing date
 20160301
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 polyanalytic function, Radó’s theorem, zero set, αanalytic function
 in
 Czechoslovak Mathematical Journal
 volume
 66
 issue
 1
 pages
 6 pages
 publisher
 Springer New York
 external identifiers

 scopus:84962850799
 wos:000373671300006
 ISSN
 00114642
 DOI
 10.1007/s1058701602381
 language
 English
 LU publication?
 yes
 id
 30be643c65e5499cb1acfa2424bd728f
 date added to LUP
 20160714 12:34:51
 date last changed
 20180107 11:21:05
@article{30be643c65e5499cb1acfa2424bd728f, abstract = {<p>Let (Formula presented.) be a bounded, simply connected ℂconvex 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 αanalytic on Ω\f<sup>−1</sup>(0), then f is αanalytic on Ω. The result is wellknown 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 = {00114642}, keyword = {polyanalytic function,Radó’s theorem,zero set,αanalytic function}, language = {eng}, month = {03}, number = {1}, pages = {5762}, publisher = {Springer New York}, series = {Czechoslovak Mathematical Journal}, title = {A pure smoothness condition for Radó’s theorem for αanalytic functions}, url = {http://dx.doi.org/10.1007/s1058701602381}, volume = {66}, year = {2016}, }