We present a formal definition of superoscillating function. We discuss the limitations of previously proposed definitions and illustrate that they do not cover the full gamut of superoscillatory behaviors. We demonstrate the suitability of the new proposal with several examples of well-known superoscillating functions that were not encompassed by previous definitions.

中文翻译：

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描述和量化超振荡的提案

我们提出了超振荡函数的正式定义。我们讨论了先前提出的定义的局限性，并说明它们并没有涵盖超振荡行为的全部范围。我们通过几个先前定义中未包含的众所周知的超振荡函数的示例来证明新提案的适用性。