On Some Operators Associated to Superoscillations
On Some Operators Associated to Superoscillations
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关于与超振荡相关的一些算子
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
J. Tollaksen
中科院分区：
文献类型：
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作者：
Y. Aharonov;F. Colombo;I. Sabadini;D. Struppa;J. Tollaksen
本文研究了与Aharonov和Berry超振荡函数有关的算子序列的收敛性。定义算子序列的主要工具是谱定理。特别是我们讨论的情况下，序列的无界自伴算子的希尔伯特空间。我们将所得结果应用到T是具有无界谱的动量算子的自伴扩张的情形。
In this paper we study the convergence of some sequences of operators associated to the Aharonov and Berry’s superoscillating functions. The main tool to define the sequences of operators is the spectral theorem. In particular we discuss the case of sequences of unbounded self-adjoint operators on a Hilbert space. We apply our results to the case where T is the self-adjoint extension of the momentum operator with unbounded spectrum.