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Positive definite hyperfunctions

Published online by Cambridge University Press:  22 January 2016

Jaeyoung Chung ,
Soon-Yeong Chung  and
Dohan Kim
Jaeyoung Chung
Affiliation:
Department of Mathematics, Kunsan National University, Kunsan, Korea
Soon-Yeong Chung
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea email: [email protected]
Dohan Kim
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea email: [email protected]
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S. Bochner proved the following theorem in [B].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 140 , December 1995 , pp. 139 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1995

References

[A] Aronszajn, N., Traces of analytic solutions of the heat equations, Astérisque 2 et 3(1973), 5–68.Google Scholar
[B] Bochner, S., Lectures on Fourier integral, Princeton University Press, Princeton, 1959.CrossRefGoogle Scholar
[CCK1] Chung, J., Chung, S. Y. and Kim, D., Une caractérisation de l’espace de Schwartz, C. R. Acad. Sci. Paris Sér. I Math., 316 (1993), 23–25.Google Scholar
[CCK2] Chung, J., Chung, S. Y. and Kim, D., A characterization for Fourier hyperfunctions, Publ. RIMS, Kyoto Univ., 30 (1994), 203–208.Google Scholar
[CK] Chung, S. -Y. and Kim, D., Distributions with exponential growth and Bochner-Schwartz theorem for Fourier hyperfunctions GARC Preprint series 92–44, 1992, (to appear in Publ. RIMS, Kyoto Univ.).Google Scholar
[GS] Gelfand, I. M. and Shilov, G. E., Generalized functions IV, Academic Press, New York, 1968.Google Scholar
[H] Hörmander, L., The analysis of linear partial differential operators, vol. 1, Springer-Verlag, Berlin-New York, 1983.Google Scholar
[Ka] Kaneko, A., Introduction to hyperfunctions, KTK Sci. Publ., Tokyo, 1988.Google Scholar
[KM] Kawai, T. and Matsuzawa, T., On the boundary value of a solution of the heat equation, Publ. RIMS, Kyoto Univ., 25 (1989), 491–498.Google Scholar
[KCK] Kim, K. H., Chung, S. -Y. and Kim, D., Fourier hyperfunctions as the boundary values of smooth of heat equations, Publ. RIMS, Kyoto Univ., 29 (1993), 289–300.Google Scholar
[M] Matsuzawa, T., A calculus approach to hyperfunctions II, Trans. Amer. Math. Soc, 313 (1990), 619–654.Google Scholar
[S] Schwartz, L., Théorie des distributions, Hermann, Paris, 1966.Google Scholar
[W] Widder, D. V., The heat equation, Academic Press, New York, 1975.Google Scholar