Regularization of hyperfunctions (Q853500)

The author treats a very interesting question for the space \(B\) of hyperfunctions which form a flabby sheaf, namely, a regularization procedure for the extension of hyperfunctions. He proves: 1. There does not exist any continuous regularization operator \(R: B(a,b)\to B[a,b)\) such that \(\pi Rg= g\), \(g\in B(a,b)\), where \(\pi: B[a,b)\to B(a,b)\) is the canonical projection. 2. Let \(H\) and \(K\) be compact subsets of \(\mathbb{R}\) with \(H\subseteq K\). Then the following statements are equivalent: (a) There exists a continuous operator \(P: B(K)\to B(H)\) with \(Pf= f\). (b) There exists a sequence of closed and open subsets \(H_n\) of \(K\) such that \(H= \bigcap^\infty_{n=1} H_n\).