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

Abtin Daghighi; Frank Wikström

doi:10.1007/s10587-016-0238-1

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

Abtin Daghighi, Frank Wikström

Matematik LTH

Linköping University

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

Sammanfattning

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 z_j (by which we mean jointly (Formula presented.) -smooth with respect to Rez_j, Imz_j). 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 α_i = 1, 1 ⩽ i ⩽ n, even when f a priori is only known to be continuous.

Originalspråk	engelska
Sidor (från-till)	57-62
Antal sidor	6
Tidskrift	Czechoslovak Mathematical Journal
Volym	66
Nummer	1
DOI	https://doi.org/10.1007/s10587-016-0238-1
Status	Published - 2016 mars 1

Ämnesklassifikation (UKÄ)

Matematisk analys

Tillgång till dokument

10.1007/s10587-016-0238-1

Citera det här

@article{30be643c65e5499cb1acfa2424bd728f,

title = "A pure smoothness condition for Rad{\'o}{\textquoteright}s theorem for α-analytic functions",

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.",

keywords = "polyanalytic function, Rad{\'o}{\textquoteright}s theorem, zero set, α-analytic function",

author = "Abtin Daghighi and Frank Wikstr{\"o}m",

year = "2016",

month = mar,

day = "1",

doi = "10.1007/s10587-016-0238-1",

language = "English",

volume = "66",

pages = "57--62",

journal = "Czechoslovak Mathematical Journal",

issn = "0011-4642",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - A pure smoothness condition for Radó’s theorem for α-analytic functions

AU - Daghighi, Abtin

AU - Wikström, Frank

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - polyanalytic function

KW - Radó’s theorem

KW - zero set

KW - α-analytic function

U2 - 10.1007/s10587-016-0238-1

DO - 10.1007/s10587-016-0238-1

M3 - Article

AN - SCOPUS:84962850799

SN - 0011-4642

VL - 66

SP - 57

EP - 62

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

IS - 1

ER -

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

Sammanfattning

Ämnesklassifikation (UKÄ)

Tillgång till dokument

Fingeravtryck

Citera det här