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<p>Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff’s results in this direction provide us with a general approximation scheme. There are situations when we need to break the interval into uneven pieces. In this paper, we explore alternative conditions to the one found by Smolyanov <i>et al</i>. such that Chernoff’s original result can be extended to unevenly distributed time intervals. Two applications concerning the foundations of quantum mechanics and the central limit theorem are presented.</p>

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Chernoff’s product formula: Semigroup approximations with non-uniform time intervals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月2日

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  • József Zsolt Bernád,
  • Andrew B. Frigyik

摘要

Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff’s results in this direction provide us with a general approximation scheme. There are situations when we need to break the interval into uneven pieces. In this paper, we explore alternative conditions to the one found by Smolyanov et al. such that Chernoff’s original result can be extended to unevenly distributed time intervals. Two applications concerning the foundations of quantum mechanics and the central limit theorem are presented.