Abstract
A way of circumventing the obstacles in the realization of original ideas by von Neumann and Gabor that are posed by the Balian–Low theorem on localization is shown, by using a special entire function with a strong exponential localization property. A square-integrable, doubly periodic and exponentially localized basis in Hilbert space of functions on C is used to solve the problem of asymptotic approximations to entire functions, in Hilbert space metrics. A new technique is suggested for numerical methods in phase-space quantum mechanics and signal processing.
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