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Erschienen in:
2019 | OriginalPaper | Buchkapitel
7. Conformal Mappings and Applications
verfasst von : Hemant Kumar Pathak
Erschienen in: Complex Analysis and Applications
Verlag: Springer Singapore
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Abstract
In the proceeding chapter, we have discussed some special types of bilinear transformations. As noted earlier that these transformations are the most powerful tools for transforming circular regions in the z-plane into circular regions or half-planes in the w-plane. In this chapter, we deal with more general situations in which we shall answer more abstract questions for determining whether and in what manner a given finite portion of an analytic surface could be represented on a portion of a plane (This well-posed problem was treated for the first time by Riemann (1826–1856) in his integral dissertation of Göttingen in 1851, which is indeed a decisive turning point in the history of Conformal Representation.).