Publication venue 'Springer Science and Business Media LLC'
Publication date 07/05/2005
Field of study Full text link Let D be a convex domain with smooth boundary in complex space and let f be a
continuous function on the boundary of D. Suppose that f holomorphically
extends to the extremal discs tangent to a convex subdomain of D. We prove that
f holomorphically extends to D. The result partially answers a conjecture by
Globevnik and Stout of 1991
Publication venue 'Springer Science and Business Media LLC'
Publication date 01/09/1995
Field of study Full text link Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46245/1/208_2005_Article_BF01461006.pd
Publication venue 'Springer Science and Business Media LLC'
Publication date
Field of study No full text
Publication venue 'Springer Science and Business Media LLC'
Publication date 01/01/2009
Field of study Get PDF summary:We solve the following Dirichlet problem on the bounded balanced domain Ω \Omega Ω with some additional properties: For p > 0 p>0 p > 0 and a positive lower semi-continuous function u u u on ∂ Ω \partial \Omega ∂ Ω with u ( z ) = u ( λ z ) u(z)=u(\lambda z) u ( z ) = u ( λ z ) for ∣ λ ∣ = 1 |\lambda |=1 ∣ λ ∣ = 1 , z ∈ ∂ Ω z\in \partial \Omega z ∈ ∂ Ω we construct a holomorphic function f ∈ O ( Ω ) f\in \Bbb O(\Omega ) f ∈ O ( Ω ) such that u ( z ) = ∫ D z ∣ f ∣ p d L D z 2 u(z)=\int _{\Bbb Dz}|f|^pd \frak L_{\Bbb Dz}^2 u ( z ) = ∫ D z ​ ∣ f ∣ p d L D z 2 ​ for z ∈ ∂ Ω z\in \partial \Omega z ∈ ∂ Ω , where D = { λ ∈ C   ∣ λ ∣ < 1 } \Bbb D=\{\lambda \in \Bbb C\:|\lambda |<1\} D = { λ ∈ C ∣ λ ∣ < 1 }
Publication venue 'Springer Science and Business Media LLC'
Publication date
Field of study No full text
Publication venue 'Springer Science and Business Media LLC'
Publication date
Field of study No full text
Publication venue
Publication date 01/01/1979
Field of study No full text
Publication venue Polska Akademia Nauk. Instytut Matematyczny PAN
Publication date 01/01/1975
Field of study No full text