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Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper, we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.


This is the submitted version of an article that later underwent peer review and was accepted for publication in Proceedings of the Royal Society A, volume 477, in 2021. The definitive publisher-authenticated version may differ and is available online at

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