Abstract
Let f be an analytic function on an open set U, and let V be an open set. We shall give various criteria when f can be extended to an analytic function on U ∪ V. The process of extending f in this way is called analytic continuation. If U, V are connected, and have in common an infinite set of points which have a point of accumulation in U ∩ V, then an analytic continuation of f to U ∪ V is uniquely determined. Indeed, if g is analytic on V and g = f on U ∩ V, then g is the only such function by Theorem 1.2 of Chapter III.
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© 1993 Springer Science+Business Media New York
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Lang, S. (1993). Schwarz Reflection. In: Complex Analysis. Graduate Texts in Mathematics, vol 103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59273-7_9
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DOI: https://doi.org/10.1007/978-3-642-59273-7_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78059-5
Online ISBN: 978-3-642-59273-7
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