Making use of the heat kernel method we deﬁne a conditionally positive deﬁnite hyperfunction and obtain a Bochner–Schwartz type theorem for hyperfunctions which generalizes both the Bochner–Schwartz type theorem for distributions of GelfandVilenkin in [GV] and our version of Bochner–Schwartz theorem for (Fourier) hyperfunctions in [CCK2, CK1].
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Dohan Kim, Jaeyoung Chung, Conditionally Positive Deﬁnite Hyperfunctions. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 385–396DOI 10.2977/PRIMS/1145475360