Analytic hypoellipticity and local solvability for a class of pseudo-differential operators with symplectic characteristics

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1. [1] L. Boutet de Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure Appl. Math. 27 (1974), 585-639. Zbl0294.35020
2. [2] L. Boutet de Monvel, A. Grigis et B. Helffer, Paramétrixes d'opérateurs pseudo-différentiels à caractéristiques multiples, Astérisque 34-35 (1976), 93-121. 
3. [3] A. Grigis and L. P. Rothschild, A criterion for analytic hypoellipticity of a class of differential operators with polynomial coefficients, Ann. Math. 118 (1983), 443-460. Zbl0541.35017
4. [4] V. V. Grushin, On a class of elliptic pseudodifferential operators degenerate on a submanifold, Math. USSR-Sb. 13 (1971), 155-185. Zbl0238.47038
5. [5] B. Helffer, Sur l'hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 dérivées), Bull. Soc. Math. France 51-52 (1977), 13-61. 
6. [6] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1980. 
7. [7] M. Kashiwara, T. Kawai and T. Oshima, Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations with multiple characteristics I, Proc. Japan Acad. 50 (1974), 420-425. Zbl0307.35081
8. [8] G. Métivier, Analytic hypoellipticity for operators with multiple characteristics, Comm. Partial Differential Equations, 6 (1981), 1-90. Zbl0455.35040
9. [9] A. Melin, Parametrix constructions for some right invariant operators on the Heisenberg group, ibid., 1363-1405. Zbl0486.35007
10. [10] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and Pseudo-Differential Operators, Lecture Notes in Math. 287, Springer, 1973, 265-529. Zbl0277.46039
11. [11] J. Sjöstrand, Parametrix for pseudodifferential operators with multiple characteristics, Ark. Mat. 12 (1974), 85-130. Zbl0317.35076
12. [12] E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math. 69 (1982), 209-216. Zbl0515.58032
13. [13] F. Treves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications, Comm. Partial Differential Equations 3 (1978), 475-642. Zbl0384.35055
14. [14] F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Vols. I, II, Plenum Press, New York and London, 1981. Zbl0453.47027