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

Mathematics (Faculty of Engineering)

Linköping University

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

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 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.

Original language	English
Pages (from-to)	57-62
Number of pages	6
Journal	Czechoslovak Mathematical Journal
Volume	66
Issue number	1
DOIs	https://doi.org/10.1007/s10587-016-0238-1
Publication status	Published - 2016 Mar 1

Subject classification (UKÄ)

Mathematical Analysis

Free keywords

polyanalytic function
Radó’s theorem
zero set
α-analytic function

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10.1007/s10587-016-0238-1

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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.",

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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

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Subject classification (UKÄ)

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