A proof of the Paley--Wiener theorem for hyperfunctions with a convex compact support by the heat kernel method
\textit{T.~Matsuzawa} [Nagoya Math.\ J.\ 108, 53--66 (1987; Zbl 0636.46047); Trans.\ Am.\ Math.\ Soc. 313, No.~2, 619--654 (1989; Zbl 0681.46042)] showed that every generalized function can be characterized by the initial value of the solutions of the heat equation with some growth condition. This is called heat kernel method. Using this method, new proofs of the Paley-Wiener type theorem were given by several mathematicians. In the present paper, the authors prove a Paley-Wiener type theorem for hyperfunctions supported by a convex compact set by the heat kernel method.
scientific article; zbMATH DE number 2124816