We study the problem of recovering a function of the form \(f(x) = \sum _{k\in \mathbb {Z}} c_k e^{-(x-k)^2}\) from its phaseless samples \(|f(\lambda )|\) on some arbitrary countable set \(\Lambda \subseteq \mathbb {R}\). For real-valued functions this is possible up to a sign for every separated set with Beurling density \(D^-(\Lambda ) >2\). This result is sharp. For complex-valued functions we find all possible solutions with the same phaseless samples.

中文翻译：

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高斯发生器在平移不变空间中的相位提取

我们研究了从其无相位样本\（f（x）= \ sum _ {k \ in \ mathbb {Z}} c_k e ^ {-（xk）^ 2} \）中恢复函数的问题。| f（\ lambda）| \）在一些任意可数集\（\ Lambda \ subseteq \ mathbb {R} \）上。对于实值函数，对于Beurling密度\（D ^-（\ Lambda）> 2 \）的每个单独集合，这最多可以有一个符号。这个结果很明显。对于复数值函数，我们找到具有相同无相样本的所有可能解。