An introduction to superoscillatory sequences
An introduction to superoscillatory sequences
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超振荡序列简介
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
D. Struppa
中科院分区：
文献类型：
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作者：
F. Colombo;I. Sabadini;D. Struppa
超振荡函数的概念，或者更准确地说是超振荡序列的概念，是阿哈罗诺夫量子力学中弱测量和弱值理论的副产品。近来，许多数学家和物理学家开始关注这类物体的数学意义，并得以开始一个关于超振荡行为的理论。毫不奇怪，这个理论是基于傅立叶分析中的一些经典结果，它与卷积方程理论有着有趣的联系。在本文中，我们将把这些连接在一个更大的背景下，并显示如何使用这个背景下产生一个大类的超振荡序列。作为一个具体的例子，我们讨论了谐振子的具有超振荡数据的柯西问题。最后，我们展示了如何将这一理论推广到多个变量的情况。
The notion of superoscillating functions, or more properly of superoscillatory sequences, is a byproduct of Aharonov’s theory of weak measurements and weak values in quantum mechanics. Recently, many mathematicians and physicists have begun to pay attention to the mathematical significance of such objects, and have been able to begin a theory of superoscillatory behavior. Not surprisingly, this theory is based on some classical results in Fourier analysis, and it displays interesting connections with the theory of convolution equations. In this paper we will put these connections in a larger context, and show how to use this context to generate a large class of superoscillating sequences. As a concrete example we discuss the Cauchy problem with superoscillatory datum for the harmonic oscillator. Finally, we show how this theory can be generalized to the case of several variables.