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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).

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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