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

• Autorzy: Tsutomu Sakurai
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 315-335

Daty

wydano

1996

Twórcy

autor

Tsutomu Sakurai

• Department of Mathematics, Saitama University, 255 Shimo-okubo, Urawa 338, Japan

Bibliografia

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• [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] 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.
• [4] V. V. Grushin, On a class of elliptic pseudodifferential operators degenerate on a submanifold, Math. USSR-Sb. 13 (1971), 155-185.
• [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] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1980.
• [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.
• [8] G. Métivier, Analytic hypoellipticity for operators with multiple characteristics, Comm. Partial Differential Equations, 6 (1981), 1-90.
• [9] A. Melin, Parametrix constructions for some right invariant operators on the Heisenberg group, ibid., 1363-1405.
• [10] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and Pseudo-Differential Operators, Lecture Notes in Math. 287, Springer, 1973, 265-529.
• [11] J. Sjöstrand, Parametrix for pseudodifferential operators with multiple characteristics, Ark. Mat. 12 (1974), 85-130.
• [12] E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math. 69 (1982), 209-216.
• [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.
• [14] F. Treves, Introduction to Pseudodifferential and Fourier Integral Operators, Vols. I, II, Plenum Press, New York and London, 1981.