On some operators associated to superoscillations (Q371867)

In connection with the theory of measurement in quantum mechanics, the authors consider the sequence of functions \(F_n (x,a)=(\cos(\frac{x}{nL})+ia\sin(\frac{x}{nL}))^n\), where \(a,L\in \mathbb R\), \(a>1\), \(L>0\), \(n\in \mathbb N\). For a selfadjoint operator \(T\), they study convergence of the sequence of operators \(F_n(T,a)\) as \(n\to \infty\), as well of the sequences corresponding to parts of spectrum of the operator \(T\). See also \textit{Y. Aharonov} et al. [J. Phys. A, Math. Theor. 44, No. 36, Article ID 365304, 16 p. (2011; Zbl 1230.42004)].