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Extension of a theorem of Duffin and Schaeffer
Let be linearly
recurrent sequences whose associated eigenvalues have arguments in
and let , where
for each . We prove that if
is bounded in a sector of its disk of convergence, it is a rational
function. This extends a very recent result of Tang and Wang, who gave the
analogous result when the sequence takes on values of finitely many
polynomials.Comment: 2 page
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