Abstract
If we associate each point z of some domain D of the z-plane with a certain complex value w according to a given law then w is called a function of z. Two geometrical interpretations of the functional relation are particularly useful. One uses one plane, the other two planes. The value w belonging to the point z (or, if more expedient, \(\bar w \) can be thought of as a vector acting on the point z; in this way a vector field is defined in the domain D. In the other interpretation, the value w associated with the point z in the z-plane is conceived as a point in another complex plane (w-plane). In this way the domain D is mapped onto a certain point set of the w-plane.
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© 1998 Springer-Verlag Berlin Heidelberg
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Pólya, G., Szegö, G. (1998). Mappings and Vector Fields. In: Problems and Theorems in Analysis I. Classics in Mathematics, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61983-0_11
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DOI: https://doi.org/10.1007/978-3-642-61983-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63640-3
Online ISBN: 978-3-642-61983-0
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