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Holomorphic mappings preserving Minkowski functionals
We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. As a con...
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Published in: | Journal of mathematical analysis and applications 2014-01, Vol.409 (2), p.643-648 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained.
As a consequence of our considerations we extend the main result of Berteloot and Patrizio (2000) [2] and we simplify its proof.
We also show how to apply our results to quasi-balanced domains. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2013.07.030 |