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On Uniqueness Sets for Expansions in Sequences of Functions Arising from Singular Generating Functions
Journal article   Open access   Peer reviewed

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

Jet Wimp
Canadian journal of mathematics, v 33(4), pp 803-816
01 Aug 1981
DOI: https://doi.org/10.4153/CJM-1981-062-2
url
https://doi.org/10.4153/cjm-1981-062-2View
Published, Version of Record (VoR)Maybe Open Access (Publisher Bronze),  Open
url
https://doi.org/10.4153/CJM-1981-062-2View
Published, Version of Record (VoR) Open

Abstract

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).

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Mathematics
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