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Sign retrieval in shift-invariant spaces with totally positive generator (2005.08678v2)
Published 18 May 2020 in math.CA
Abstract: We show that a real-valued function $f$ in the shift-invariant space generated by a totally positive function of Gaussian type is uniquely determined, up to a sign, by its absolute values ${|f(\lambda)|: \lambda \in \Lambda }$ on any set $\Lambda \subseteq \mathbb{R}$ with lower Beurling density $D{-}(\Lambda)>2$.
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