Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T15:00:52.807Z Has data issue: false hasContentIssue false
  • English
  • Français

A calculus approach to hyperfunctions III

Published online by Cambridge University Press:  22 January 2016

Tadato Matsuzawa
Tadato Matsuzawa*
Affiliation:
Department of Mathematics, Meijo University, Tenpaku-kn, Nagoya 468, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the previous papers, [18] and [19], we have given some basis of a calculus approach to hyperfunctions. We have taken hyperfunctions with the compact support as initial values of the solutions of the heat equation. More precisely, let A′[K] be the space of analytic functionals supported by a compact subset K of Rn and let E(x, t) be the n-dimensional heat kernel given by

.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 133 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Aronszajn, N., Preliminary notes for “Traces of analytic solutions of the heat equation” and Traces of analytic solutions of the heat equation, Colloque International C.N.R.S. sur les équations aux dérivées partielles linéaires, 2–3 (1973), 5–68.Google Scholar
[2] Bony, J. M., Equivalence des diverses notions de spectre singulier analytique, Séminaire Goulaouic-Schwartz 1976-1977, Exposé No. 3.Google Scholar
[3] Bros, J. and Iagolnitzer, D., Support essentiel et structure analytique des distributions, Séminaire Goulaouic-Lions-Schwartz 1975, Exposé No. 18.Google Scholar
[4] Gel’fand, I. M. and Shilov, G. E., Generalized functions, Vol. 2, Academic press, New York-London, 1968.Google Scholar
[5] Hashimoto, S., Matsuzawa, T. and Morimoto, Y., Opérateurs pseudodifferentiels et classes de Gevrey, Comm. Partial Differential Equations, 8 (12) (1983), 1277–1289.CrossRefGoogle Scholar
[6] Hörmander, L., Pseudodifferential operators and hypoelliptic equations, Proc. symposium on singular integrals, Amer. Math. Soc., 10 (1967), 138–183.CrossRefGoogle Scholar
[7] Hörmander, L., The analysis of linear partial differential operators, Vol. 1, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1983.Google Scholar
[8] Iwasaki, C., Gevrey-hypoellipticity and pseudo-differential operators on Gevrey class, Lecture Notes in Math. Vol. 1256, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1986, 281–293.Google Scholar
[9] Kajitani, K. and Wakabayashi, S., Hypoelliptic operators in Gevrey classes, to appear.Google Scholar
[10] Kashiwara, M., Introduction to the theory of hyperfunctions, Sem. on microlocal analysis, Princeton Univ. Press, Princeton, N. J., 1979, 3–38.Google Scholar
[11] Kawai, T. and Matsuzawa, T., On the boundary value of the solution of the heat equation, to appear in Publ. RIMS, Kyoto Univ., 25 (1989).Google Scholar
[12] Komatsu, H., Ultradistributions I; Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo, Sect. IA, 20 (1973), 25–105.Google Scholar
[13] Komatsu, H., Ultradistributions II; The kernel theorem and ultradistributions with support in a submanifold, J. Fac. Sci. Univ. Tokyo, Sect. IA, 24 (1977), 607–628.Google Scholar
[14] Komatsu, H., Introduction to the theory of generalized functions (in Japanese), Iwanami Shoten, 1978.Google Scholar
[15] Martineau, A., Les hyperfonctions de M. Sato, Séminaire Bourbaki 1960-1961, Exposé No. 214.Google Scholar
[16] Matsuzawa, T., Gevrey hypoellipticity of a class of pseudodifferential operators, Tôhoku Math. J., 39 (1987), 447–464.CrossRefGoogle Scholar
[17] Matsuzawa, T., Hypoellipticity in ultradistribution spaces, J. Fac. Sci. Univ. Tokyo, Sect. IA, 34 (1987), 779–790.Google Scholar
[18] Matsuzawa, T., A calculus approach to hyperfunctions I, Nagoya Math. J., 108 (1987), 53–66.CrossRefGoogle Scholar
[19] Matsuzawa, T., A calculus approach to hyperfunctions II, Trans. Amer. Math. Soc., 313, No. 2 (1989), 619–654.CrossRefGoogle Scholar
[20] Miyake, M., Solvability of systems of ordinary defferential equations in the space of Aronszajn and the determinant over the Weyl algebra, to appear.Google Scholar
[21] Shinkai, K. and Taniguchi, K., Fundamental solution for a degenerate hyperbolic operator in Gevrey classes, to appear.Google Scholar
[22] Sjöstrand, J., Propagation of analytic singularities for second order Dirichlet problems, Comm. Partial Differential Equations, 5(1) (1980), 41–94.CrossRefGoogle Scholar
[23] Sjöstrand, J., Singularités analytiques microlocales, Astérisques, 95 (1982), 1–166.Google Scholar
[24] Taniguchi, K., On multi-products of pseudodifferential operators in Gevrey classes and its application to Gevrey hypoellipticity, Proc. Japan Acad., Ser. A (1985), 291–293.CrossRefGoogle Scholar
[25] Treves, F., Introducton to pseudodifferential and Fourier integral operators, Vol. 1, Plenum Press, New York-London, 1981.Google Scholar