Search for dissertations about: "domain of holomorphy"
Found 5 swedish dissertations containing the words domain of holomorphy.
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1. Algebras of bounded holomorphic functions
Abstract : Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. READ MORE
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2. Envelopes of holomorphy for bounded holomorphic functions
Abstract : Some problems concerning holomorphic continuation of the class of bounded holomorphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Gleason’s Problem for H°°(Ω) cannot be solved. READ MORE
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3. Infinite dimensional holomorphy in the ring of formal power series : partial differential operators
Abstract : We study holomorphy in the ring of formal power series in an infinite number of variables. Thus we restrict our study to (infinite dimensional) holomorphy on sequence spaces and we show that we obtain a rich theory without requiring any topological structure on the domain space. We make a comprehensive PDO-study for the spaces under consideration. READ MORE
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4. On Propagation of Boundary Continuity for Domains in Complex Space
Abstract : We consider continuity properties of analytic functions in bounded domains in complex space, focusing on the following two questions:Question 1. Given a bounded domain G in complex affine n-space. READ MORE
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5. Holomorphic extension and schlichtness on tube manifolds
Abstract : We first investigate the holomorphic extension of some classical and accessible classes of domains in $\mathbb{C}^n$ to know to what extent their envelopes are constructive. We give alternative proofs to some of the classical theorems using only first-principle arguments and without involving higher Stein geometry. READ MORE