Uniqueness of nonArchimedean entire functions sharing sets of values counting multiplicity
Authors:
William Cherry and ChungChun Yang
Journal:
Proc. Amer. Math. Soc. 127 (1999), 967971
MSC (1991):
Primary 11S80, 30D35
MathSciNet review:
1487362
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Abstract: A set is called a unique range set for a certain class of functions if each inverse image of that set uniquely determines a function from the given class. We show that a finite set is a unique range set, counting multiplicity, for nonArchimedean entire functions if and only if there is no nontrivial affine transformation preserving the set. Our proof uses a theorem of Berkovich to extend, to nonArchimedean entire functions, an argument used by Boutabaa, Escassut, and Haddad to prove this result for polynomials
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Additional Information
William Cherry
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Address at time of publication:
Department of Mathematics, University of North Texas, Denton, Texas 76203
ChungChun Yang
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email:
mayang@uxmail.ust.hk
DOI:
http://dx.doi.org/10.1090/S0002993999047899
PII:
S 00029939(99)047899
Received by editor(s):
July 18, 1997
Additional Notes:
Financial support for the first author was provided by National Science Foundation grants DMS9505041 and DMS9304580
The second author’s research was partially supported by a UGC grant of Hong Kong.
Communicated by:
David E. Rohrlich
Article copyright:
© Copyright 1999 American Mathematical Society
