We show that a Bessel sequence \(B_\psi \) of integer translates of a square integrable function \(\psi \in L^2(\mathbb {R})\) has the Besselian property if and only if its periodization function \(p_\psi \) is bounded from below. We also give characterizations of Besselian and Hilbertian properties of a general sequence \(B_\psi \) of integer translates in terms of the classical notion of sequence dominance.

中文翻译：

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移位不变空间中的序列优势

我们证明，当且仅当它的周期化函数时，方可积函数\（\ psi \ in L ^ 2（\ mathbb {R}）\）的整数平移的贝塞尔序列\（B_ \ psi \）具有Besselian属性\（p_ \ psi \）从下面限制。我们还根据序列优势的经典概念，给出了整数转换的一般序列\（B_ \ psi \）的Besselian和Hilbertian性质的表征。