- Title
- Extension of a theorem of Duffin and Schaeffer
- Creator
- Coons, Michael
- Relation
- Journal of Integer Sequences Vol. 20, no. 17.9.4
- Relation
- https://cs.uwaterloo.ca/journals/JIS/VOL20/Coons/coons7.html
- Publisher
- University of Waterloo
- Resource Type
- journal article
- Date
- 2017
- Description
- Let r1,..., rs: Zn≥0 → C be linearly recurrent sequences whose associated eigenvalues have arguments in πQ and let F(z) := Σn ≥ 0 f(n)zn, where f(n) ∈ {r1(n),..., rs(n)} for each n ≥ 0. We prove that if F(z) is bounded in a sector of its disk of convergence, then it is a rational function. This extends a very recent result of Tang and Wang, who gave the analogous result when the sequence f(n) takes on values of finitely many polynomials.
- Subject
- linearly recurrent sequences; eigenvalues and eigenfunctions; polynomials
- Identifier
- http://hdl.handle.net/1959.13/1352561
- Identifier
- uon:30912
- Identifier
- ISSN:1530-7638
- Rights
- © 2017 The Author(s).
- Language
- eng
- Full Text
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|---|---|---|---|---|---|---|---|
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