论文标题
整个功能的阶段检索及其对Gabor阶段检索的影响
Phase retrieval of entire functions and its implications for Gabor phase retrieval
论文作者
论文摘要
我们表征了所有有限顺序的整个函数对，其大小通过Hadamard分解定理在复杂平面上的两个任意线上一致。在此基础上，我们还表征了所有二阶对整个功能的表征，其幅度在无限的等距平行线上一致。此外，我们表明，整个功能在三个平行线上的大小，其距离在理性上是独立的，独特地确定了函数到全球阶段，并且存在一个第一阶整个函数，其在行上的大小$ \ mathbb {r} + \ \ \ \ \ tfrac {\ trm {\ mathrm {i}} {i}} {z n} {z n} {z n}所有正整数$ n $。我们的结果对Gabor阶段检索有直接影响。
We characterise all pairs of finite order entire functions whose magnitudes agree on two arbitrary lines in the complex plane by means of the Hadamard factorisation theorem. Building on this, we also characterise all pairs of second order entire functions whose magnitudes agree on infinitely many equidistant parallel lines. Furthermore, we show that the magnitude of an entire function on three parallel lines, whose distances are rationally independent, uniquely determines the function up to global phase, and that there exists a first order entire function whose magnitude on the lines $\mathbb{R} + \tfrac{\mathrm{i}}{n} \mathbb{Z}$ does not uniquely determine it up to global phase, for all positive integers $n$. Our results have direct implications for Gabor phase retrieval.
