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On Some Operators Associated to Superoscillations |
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| Authors: | Y. Aharonov F. Colombo I. Sabadini D. C. Struppa J. Tollaksen |
| Affiliation: | 1. Schmid College of Science and Technology and Institute for Quantum Studies, Chapman University, Orange, CA, 92866, USA 2. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, 20133, Milan, Italy 3. Schmid College of Science and Technology, Chapman University, Orange, CA, 92866, USA |
| Abstract: | 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. |
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