Displaying similar documents to “On the connectedness of boundary and complement for domains”

Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions

Thomas Patrick Pawlaschyk (2016)

Annales Polonici Mathematici

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We introduce the notion of the Shilov boundary for some subfamilies of upper semicontinuous functions on a compact Hausdorff space. It is by definition the smallest closed subset of the given space on which all functions of that subclass attain their maximum. For certain subfamilies with simple structure we show the existence and uniqueness of the Shilov boundary. We provide its relation to the set of peak points and establish Bishop-type theorems. As an application we obtain a generalization...

On propagation of boundary continuity of holomorphic functions of several variables

Salla Franzén, Burglind Jöricke (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements...

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.