Sets of uniqueness and sets of multiplicity
نویسندگان
چکیده
منابع مشابه
Sets of extended uniqueness and σ - porosity
We show that there exists a closed non-σ-porous set of extended uniqueness. We also give a new proof of Lyons’ theorem, which shows that the class of H(n)-sets is not large in U0.
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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 non-Archimedean entire functions if and only if there is no non-trivial affine transformation preserving the set. Our proof uses a theorem of Berkovich to extend, to ...
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If f(z) satisfies (1) but meets the weaker restriction that/(z) is regular for (R(z) ̂ 0, we shall say that it belongs to K*(a, c). A set A is said to be a set of uniqueness for a class K of functions provided that the only function/(z) in K such that/(a) =0 for each a in A is the null function /(z)=0. Finally, we say that A has blocks of ratio <p if there is an increasing sequence [w*]*=o,i,2,-...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 2002
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc56-0-5