Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

Description of simple exceptional sets in the unit ball

Piotr Kot — 2004

Czechoslovak Mathematical Journal

For z B n , the boundary of the unit ball in n , let Λ ( z ) = { λ | λ | 1 } . If f 𝕆 ( B n ) then we call E ( f ) = { z B n Λ ( z ) | f ( z ) | 2 d Λ ( z ) = } the exceptional set for f . In this note we give a tool for describing such sets. Moreover we prove that if E is a G δ and F σ subset of the projective ( n - 1 ) -dimensional space n - 1 = ( n ) then there exists a holomorphic function f in the unit ball B n so that E ( f ) = E .

Boundary functions in L 2 H ( 𝔹 n )

Piotr Kot — 2007

Czechoslovak Mathematical Journal

We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function u which is lower semi-continuous on 𝔹 n we give necessary and sufficient conditions in order that there exists a holomorphic function f 𝕆 ( 𝔹 n ) such that u ( z ) = | λ | < 1 f ( λ z ) 2 d 𝔏 2 ( λ ) .

Boundary functions on a bounded balanced domain

Piotr Kot — 2009

Czechoslovak Mathematical Journal

We solve the following Dirichlet problem on the bounded balanced domain Ω with some additional properties: For p > 0 and a positive lower semi-continuous function u on Ω with u ( z ) = u ( λ z ) for | λ | = 1 , z Ω we construct a holomorphic function f 𝕆 ( Ω ) such that u ( z ) = 𝔻 z | f | p d 𝔏 𝔻 z 2 for z Ω , where 𝔻 = { λ | λ | < 1 } .

Page 1

Download Results (CSV)