Global analytic and Gevrey surjectivity of the Mizohata operator $D_2+i{x}_2^{2k}{D}_1$

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1. [1] R.W. Braun - R. Meise - D. Vogt. “Applications of the projiective limit functor to convolution and partial differential equations”, Proceeding of the NATO ASW on “Fréchet spaces”, Istanbul August 1988, D. Reidel Publishing Comp., (to appear). Zbl0726.46022
2. [2] L. Cattabriga. “Solutions in Gevrey spaces of partial differential equations with constant coefficients”, Astérisque 89-90 (1981), 129-151. Zbl0496.35018MR84h:35030
3. [3] L. Cattabriga. “On the surjectivity of differential polynomials on Gevrey spaces”, Rend. Sem. Mat. Univ. Politec. Torino, Fasc. speciale, Convegno “Linear partial and pseudo-differential operators”, Torino, 30 Sett.-2 Ott. 1982, 41 (1983), 81-89. Zbl0561.35008MR85f:35046
4. [4] E.De Giorgi. “Solutions analytiques des équations aux dérivées partielles à coefficients constants”, Séminaire Goulaouic-Schwartz 1971-1972, Equations aux dérivées partielles et analyse fonctionnelle, Exp. N. 29, Ecole Polytech. Centre de Math. Paris 1972. Zbl0244.35017
5. [5] E. De Giorgi - L. Cattabriga. “Una dimostrazone diretta dell'esistenza di soluzioni analitiche nel piano reale di equazioni a derivate parziali a coefficienti costanti”, Boll. Un. Mat. Ital. (4) 4 (1971), 1015-1027. Zbl0224.35018MR52 #3702
6. [6] L. Ehrenpreis. “Lewy's operator and its ramifications”, J. Funct. Analysis 68 (1986), 329-365. Zbl0638.35002MR87j:35018
7. [7] J. Friberg. “Estimates for partially hypoelliptic differential operators”, Medd. Lund Univ. Mat. Sem. 17 (1963), 1-93. Zbl0139.28403MR28 #349
8. [8] L. Hörmander. “On the existence of real analytic solutions of partial equations with constant coefficients”, Inventiones Math. 21 (1973), 151-182. Zbl0282.35015MR49 #817
9. [9] L. Hörmander. “The analysis of linear partial differential operators”, Springer-Verlag, (1983), vol. IV. Zbl0521.35002
10. [10] T. Kawai, “On the global existence of real analytic solutions of linear differential equations” I and II, J. Math. Soc. Japan 24 (1972), 481-517; 25 (1973), 644-647. Zbl0259.35062
11. [11] T. Kawai, “On the global existence of real analytic solutions and hyperfunction solutions of linear differential equations”, Publ. RIMS Kyoto University 555 (1986). Zbl0618.35002MR87k:58249
12. [12] H. Komatsu, “An analogue of the Cauchy-Kowalevsky theorem for ultradifferentiable functions and a division theorem of ultradistributions as its dual”, J. Fac. Sci. Univ. Tokyo, Sec. IA 26 (1979), 239-254. Zbl0424.46032MR81i:35008
13. [13] S. Mizohata, «Solutions nulles et solutions non analytiques», J. Math. Kyoto Univ. 1 (1962), 271-302. Zbl0106.29601MR26 #440
14. [14] L. Rodino, “On linear partial differential operators with multiple characteristics”, Proceedings Conf. on partial Differential Equations, Holzhau (GDR), 1988, Teubner Text zur Mathematik. Zbl0681.35093
15. [15] G. Zampieri, “An application of the fundamental principle of Ehrenpreis to the existence of global Gevrey solutions of linear differential equations”, Boll. Un. Mat. Ital. (6) V B (1986), 361-392. Zbl0624.35011MR88a:35044