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A proof of Paley-Wiener theorem for Fourier hyperfunctions with support in a proper convex cone by the heat kernel method
by
Masanori Suwa
Ebie-Neriya 1-2, Shimminato-shi, Toyama 933-0293 Japan
Coauthors: Kunio Yoshino
T.Kawai constructed the theory of Fourier hyperfunctions and gave Paley-Wiener theorem for this space. In 1987, T.Matsuzawa gave a new proof of Paley-Wiener theorem for hyperfunctions supported by a ball by the heat kernel method. S.Lee and S.-Y.Chung gave a proof of Paley-Wiener-Schwartz theorem for distributions supported by a convex compact set by the heat kernel method. M.Suwa and K.Yoshino treated the case of tempered distributions supported by a proper convex cone and the case of hyperfunctions supported by a convex compact set by the heat kernel method, and M.Suwa treated the case of distributions of exponential growth supported by a proper convex cone. In this paper we shall give a new proof of Paley-Wiener theorem for Fourier hyperfunctions supported by a proper convex cone by the heat kernel method.
Date received: May 26, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqw-97.