Abstract
In Chapter 12 we proved approximation theorems for compact sets; we now prove their analogues for regions. We pose the following question:
When are regions D, D’ with D ⊂ D’ a Runge pair? That is, when can every function holomorphic in D be approximated compactly by functions holomorphis in D’?
Jede eindeutige analytische Function kann durch eine einzige unendliche Summe von rationalen Functionen in ihrem ganzen Gültigkeitsbereich dargestellt werden. (Every single-valued analytic function can be represented by a single infinite sum of rational functions in its whole region of validity.)
— C. Runge, 1884
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Remmert, R. (1998). Runge Theory for Regions. In: Classical Topics in Complex Function Theory. Graduate Texts in Mathematics, vol 172. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2956-6_13
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DOI: https://doi.org/10.1007/978-1-4757-2956-6_13
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