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In this paper we discuss the approximation of hyperfunctions in one variable using sequences of low frequency hyperfunctions. In particular, we show that this superoscillation property holds for compactly supported hyperfunctions. Finally, we show that the approximation is also possible for tempered hyperfunctions.
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Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger, Superoscillating Sequences and Hyperfunctions. Publ. Res. Inst. Math. Sci. 55 (2019), no. 4, pp. 665–688