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Media type:
E-Article
Title:
BOUNDARY DIFFERENTIAL RELATIONS FOR HOLOMORPHIC FUNCTIONS ON THE DISC
Contributor:
ČERNE, MIRAN;
ZAJEC, MATEJ
imprint:
American Mathematical Society, 2011
Published in:Proceedings of the American Mathematical Society
Language:
English
DOI:
10.1090/S0002-9939-2010-10469-0
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
<p>The existence of solutions of boundary differential relations for holomorphic functions on the disc Δ is considered. First we prove that for an arbitrary continuous positive function Φ on the complex planeℂ there exists a disc algebra function f Є A(Δ) such that |f'| = Φ(f) on ∂Δ. Assuming some smoothness, the existence result is also proved for a quite general differential relation p(ξ, f'(ξ)) = Φ(ξ, f(ξ), ξ Є ∂Δ, where p is a defining function for a family of Jordan curves in ℂ containing point 0 in its interior and Φ is a bounded positive function on ∂Δ × ℂ.</p>