Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T23:13:29.750Z Has data issue: false hasContentIssue false
  • English
  • Français

Solvability of systems of ordinary differential equations in the space of Aronszajn and the determinant over the Weyl algebra

Published online by Cambridge University Press:  22 January 2016

Masatake Miyake
Masatake Miyake*
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Chikusa-ku, Nagoya, 464, 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.

N. Aronszajn introduced in [4] an abstract Frechét space R (0<R≤∞), which is isomorphic to the space of analytic solutions of the heat equation in if 0 < R ∞, and in if R = ∞, and called it the space of traces of analytic solutions of the heat equation. Hereafter, we call it the space of traces, shortly.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 117 , March 1990 , pp. 207 - 225
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Adjamagbo, K., Déterminant sur des anneaux filtrés, C.R. Acad. Sci. Paris, 293 (1981), 447–449.Google Scholar
[2] Adjamagbo, K., Théorèmes d’indece pour les systèmes généraux d’equations différentielles linéaires, Séminaire de J. Vaillant de Univ. Paris 6, (1982-83), 134–165.Google Scholar
[3] Aronszajn, N., Preliminary notes for “Traces of analytic solutions of the heat equation”, Colloque International C.N.R.S. sur les équations aux dérivées partielles linéaire, Astérisque, 2-3 (1973), 5–34.Google Scholar
[4] Aronszajn, N., Traces of analytic solutions of the heat equation, ibid., 2-3 (1973), 35–68.Google Scholar
[5] Baouendi, M. S., Solvability of partial differential equations in the traces of analytic solutions of the heat equation, Amer. Jour. Math., 97 (1976), 983–1005.CrossRefGoogle Scholar
[6] Björk, J. E., Rings of Differential Operators, North-Holland Publ. Co., Amsterdam-Oxford-New York, 1979.Google Scholar
[7] Dieudonné, J., Les déterminants sur un corp non commutatif, Bull. Soc. Math. France, 71 (1943), 27–45.CrossRefGoogle Scholar
[8] Komatsu, H., Introduction to the theory of hyperfunctions (in Japanese), Iwanami Publ., Tokyo, 1978.Google Scholar
[9] Miyake, M., On the determinant of matrices of ordinary differential operators and an index theorem, Funk. Ekvac., 26 (1983), 155–171.Google Scholar
[10] Miyake, M., On the irregularity for general systems of differential equations in the complex domain, ibid., 26 (1983), 211–230.Google Scholar
[11] Sato, M. and Kashiwara, M., The determinant of pseudo-differential operators, Proc. Japan Acad., 51 (1975), 17–19.Google Scholar
[12] Schapira, P., Microdifferential systems in the complex domain, Springer-Verlag, Berlin-Heiderberg-New York-Tokyo, 1985.CrossRefGoogle Scholar