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On Uniqueness Sets for Expansions in Sequences of Functions Arising from Singular Generating Functions

Published online by Cambridge University Press:  20 November 2018

Jet Wimp
Jet Wimp*
Affiliation:
Drexel University, Philadelphia, Pennsylvania
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Let {pn(z)}; be a sequence of functions analytic in a region D. A problem in analysis which has received much attention is the following: describe the sets Z ⊂ D for which

(1)

implies hn is 0 for all n, (To make the problem interesting, only those situations are studied where finite subsets of the pn (z) are linearly independent in D.) Another way of phrasing this is: Characterize the uniqueness sets of pn (z), a uniqueness set Z being a set in D such that the restriction of {pn (z)}; to Z is linearly independent. If Z is not a uniqueness set then for some {hn}; not all 0, we have

(2)

This formula is called a non-trivial representation of 0 (on Z).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981 , pp. 803 - 816
Copyright
Copyright © Canadian Mathematical Society 1981

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