Asymptotic first boundary value problem for holomorphic functions of several complex variables

In 1955, Lehto showed that, for every measurable function $\psi $ on the unit circle ${\mathbb T}$ , there is a function f holomorphic in the unit disc ${{\mathbb D}}$ , having $\psi $ as radial limit a.e. on ${\mathbb T}$ . We consider an analogous boundary value problem, where the unit disc is rep...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 65; no. 2; pp. 361 - 380
Main Authors Gauthier, Paul M., Shirazi, Mohammad
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.06.2022
Cambridge University Press
Subjects
Analytic functions
Asymptotic properties
Boundary value problems
Complex variables
Mathematical analysis
30E10
holomorphic functions
32E30
32A40
complex approximation
Boundary values
30E25
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Summary:In 1955, Lehto showed that, for every measurable function $\psi $ on the unit circle ${\mathbb T}$ , there is a function f holomorphic in the unit disc ${{\mathbb D}}$ , having $\psi $ as radial limit a.e. on ${\mathbb T}$ . We consider an analogous boundary value problem, where the unit disc is replaced by a Stein domain on a complex manifold and radial approach to a boundary point p is replaced by (asymptotically) total approach to p.
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439521000321