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Showing 1 to 3 of 3 for “"Carathéodory"”.
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Lifting Module Maps Between Different Noncommutative Domain Algebras
<p>The classical Carathéodory interpolation problem is the following: let n be a natural number, a<sub>0</sub>, a<sub>1</sub>, . . . , a<sub>N</sub> be complex numbers, and <strong>D</strong> the unit disk. When does there exist an analytic function F : <strong>D</strong> → <strong>C</strong> and …
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A Synthesis of Classical Boundary Theorems
… points, Julia’s Theorem and<br />the Julia-Carathéodory Theorem. This thesis serves as a synthesis of these boundary<br />theorems in order to fill a gap in the overarching literature.<br /><br />
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Generalised Loewner Evolutions and their driving measures
… all three cases Loewner chains are compact under Carathéodory convergence, i.e. uniform convergence on compact subsets of [0, T] x D, resp. [0, T] x H. This corresponds to a tightness property of the underlying driving measures. In all cases these two facts imply that the Loewner-Kufarev Map …