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

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1. 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. Zbl0734.35164
2. [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. Zbl0701.35014
3. [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. Zbl0676.35052MR956023
4. [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. Zbl0725.35113MR1041717
5. [5] P. Hartman, Ordinary Differential Equations, John Wiley, 1964. Zbl0125.32102MR171038
6. [6] S. Hashimoto - T. Matsuzawa - Y. Morimoto, Operateurs pseudo-differentiels et classes de Gevrey, C.P.D.E., (1983), pp. 1277-1289. Zbl0525.35086MR711439
7. [7] K. Kajitani, Fundamental solution of Cauchy problem for hyperbolic systems and Gevrey classes, Tsukuba J. Math., 1 (1977), pp. 163-193. Zbl0402.35068MR481569
8. [8] K. Kajitani - S. Wakabayashi, Microhyperbolic operators in Gevrey classes, Publ. RIMS (to appear). Zbl0705.35158MR1003785
9. [9] H. Kumano-Go, Pseudo-differential Operators, M.I.T. Press, 1981. Zbl0489.35003
10. [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. Zbl0665.35006MR925250
11. [11] S. Mizohata, On the Cauchy Problem, Science Press, Bejing, 1985. Zbl0616.35002MR860041
12. [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. Zbl0631.35052MR873208
13. [13] L. Rodino - L. Zanghirati, Pseudo-differential operators with multiple characteristics and Gevrey singularities, C.P.D.E., 11 (1986), pp. 673-711. Zbl0597.58034MR837927
14. [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. Zbl0574.35082MR759680
15. [15] K. Taniguchi, Pseudo-differential operators acting on ultradistributions, Math. Japonica, 30 (1985), pp. 719-741. Zbl0584.35104
16. [16] L. Zanghirati, Pseudo-differential operators of infinite order and Gevrey classes, Ann. Univ. Ferrara - sez. VII - Sc. Mat. (1985), pp. 197-219. Zbl0601.35110

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