Fourier integral operators of infinite order on ${𝒟}_{{L}^{2}}^{\left\{\sigma \right\}}\left({𝒟}_{{L}^{2}}^{{\left\{\sigma \right\}}^{\text{'}}}\right)$ with an application to a certain Cauchy problem
Rendiconti del Seminario Matematico della Università di Padova, Tome 84 (1990) , p. 71-82
URL stable : http://www.numdam.org/item?id=RSMUP_1990__84__71_0

### Bibliographie

1] R. Agliardi, Pseudo-differential operators of infinite order on D{σ}L2),(D{σ)'L2), and applications to the Cauchy problem for some elementary operators, to appear on Ann. di Mat. Pura e Appl. Zbl 0734.35164

[2] L. Cattabriga, Some remarks on the well-posedness of the Cauchy problem in Gevrey spaces, in Partial Differential Equations and the Calculus of Variations: Essays in honour of Ennio De Giorgi. Zbl 0701.35014

[3] L. Cattabriga - D. MARI, Parametrix of infinite order on Gevrey spaces to the Cauchy problem for hyperbolic operators with one constant multiple characteristics, Ricerche di Mat., Suppl., 36 (1987), pp. 127-147. MR 956023 | Zbl 0676.35052

[4] L. Cattabriga - L. Zanghirati, Fourier integral operators of infinite order on Gevrey spaces-Applications to the Cauchy problem for certain hyperbolic operators, to appear on Journal of Math. of Kyoto Univ. MR 1041717 | Zbl 0725.35113

[5] P. Hartman, Ordinary Differential Equations, John Wiley, 1964. MR 171038 | Zbl 0125.32102

[6] S. Hashimoto - T. Matsuzawa - Y. Morimoto, Operateurs pseudo-differentiels et classes de Gevrey, C.P.D.E., (1983), pp. 1277-1289. MR 711439 | Zbl 0525.35086

[7] K. Kajitani, Fundamental solution of Cauchy problem for hyperbolic systems and Gevrey classes, Tsukuba J. Math., 1 (1977), pp. 163-193. MR 481569 | Zbl 0402.35068

[8] K. Kajitani - S. Wakabayashi, Microhyperbolic operators in Gevrey classes, Publ. RIMS (to appear). MR 1003785 | Zbl 0705.35158

[9] H. Kumano-Go, Pseudo-differential Operators, M.I.T. Press, 1981. Zbl 0489.35003

[10] S. Misohata, On the Cauchy problem for hyperbolic equations and related problems-micro-local energy methods, Proc. Taniguchi Intern. Sympos. on Hyperbolic Equations and Related Topics, Kataka, 1984, pp. 193-233. MR 925250 | Zbl 0665.35006

[11] S. Mizohata, On the Cauchy Problem, Science Press, Bejing, 1985. MR 860041 | Zbl 0616.35002

[12] Y. Morimoto - K. Taniguchi, Propagation of wave front sets of solutions of the Cauchy problem for hyperbolic equations in Gevrey classes, Osaka J. of Math., 23 (1986), pp. 765-814. MR 873208 | Zbl 0631.35052

[13] L. Rodino - L. Zanghirati, Pseudo-differential operators with multiple characteristics and Gevrey singularities, C.P.D.E., 11 (1986), pp. 673-711. MR 837927 | Zbl 0597.58034

[14] K. Taniguchi, Fourier integral operators in Gevrey classes on Rn and the fundamental solution for a hyperbolic operator, Publ. R.I.M.S., 20 (1984), pp. 491-542. MR 759680 | Zbl 0574.35082

[15] K. Taniguchi, Pseudo-differential operators acting on ultradistributions, Math. Japonica, 30 (1985), pp. 719-741. Zbl 0584.35104

[16] L. Zanghirati, Pseudo-differential operators of infinite order and Gevrey classes, Ann. Univ. Ferrara - sez. VII - Sc. Mat. (1985), pp. 197-219. Zbl 0601.35110