Continuity of some operators arising in the theory of superoscillations
Continuity of some operators arising in the theory of superoscillations
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DOI：
10.1007/s40509-018-0159-9
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发表时间：
2018-09-01
影响因子：
0.8
通讯作者：
Struppa, D. C.
中科院分区：
文献类型：
--
作者：
Aoki, T.;Colombo, F.;Struppa, D. C.
超振荡的研究自然会导致分析一大类卷积算子作用于整个函数空间。特别是，关键点通常是证明这些算子在适当的空间上的连续性。目前文献中的大多数论文利用泛函分析的抽象方法来建立这种连续性。在本文中，另一方面，我们依赖于一些最近的进展，在整个功能的研究，提供明确的证明，这样的运营商的连续性。为了证明这些显式方法的适用性和灵活性，我们将使用它们来研究与二次哈密顿量相关的超振荡的重要情况。该文件还包含一个有趣的开放式问题的列表，我们也收集了，为了方便读者，一些著名的结果，和他们的证明，伽玛和米塔格-莱弗勒函数，经常使用在我们的计算。
The study of superoscillations naturally leads to the analysis of a large class of convolution operators acting on spaces of entire functions. In particular, the key point is often the proof of the continuity of these operators on appropriate spaces. Most papers in the current literature utilize abstract methods from functional analysis to establish such continuity. In this paper, on the other hand, we rely on some recent advances in the study of entire functions, to offer explicit proofs of the continuity of such operators. To demonstrate the applicability and the flexibility of these explicit methods, we will use them to study the important case of superoscillations associated with quadratic Hamiltonians. The paper also contains a list of interesting open problems, and we have collected as well, for the convenience of the reader, some well-known results, and their proofs, on Gamma and Mittag-Leffler functions that are often used in our computations.