On mapping properties of monogenic functions
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K. Gürlebeck
guerlebe@fossi.uni-weimar.de
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J. Morais
jmorais@mat.ua.pt
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Abstract
Main goal of this paper is to study the description of monogenic functions by their geometric mapping properties. At first monogenic functions are studied as general quasi-conformal mappings. Moreover, dilatations and distortions of these mappings are estimated in terms of the hypercomplex derivative. Then pointwise estimates from below and from above are given by using a generalized Bohr‘s theorem and a Borel-Carathéodory theorem for monogenic functions. Finally it will be shown that mono- genic functions can be defined as mappings which map infinitesimal balls to special ellipsoids.
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Published
2009-03-01
How to Cite
[1]
K. Gürlebeck and J. Morais, “On mapping properties of monogenic functions”, CUBO, vol. 11, no. 1, pp. 73–100, Mar. 2009.
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