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A class of hypoelliptic pseudodifferential operators with double characteristics. (English) Zbl 0306.35032


MSC:

35H10 Hypoelliptic equations
35S05 Pseudodifferential operators as generalizations of partial differential operators
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References:

[1] Boutet de Monvel, L.: Hypoelliptic operators with double characteristics and related pseudo-differential operators. Comm. Pure Appl. Math.27, 585-639 (1974) · Zbl 0294.35020 · doi:10.1002/cpa.3160270502
[2] Boutet de Monvel, L., Trèves, F.: On a class of pseudo-differential operators with double characteristics. Inventiones math.24, 1-34 (1974) · Zbl 0281.35083 · doi:10.1007/BF01418785
[3] Calderón, A. P., Vaillancourt, R.: A class of bounded pseudo-differential operators. Proc. Nat. Acad. Sci. USA69, 1185-1187 (1972) · Zbl 0244.35074 · doi:10.1073/pnas.69.5.1185
[4] Grigis, A.: Hypoellipticité pour une class d’opérateurs pseudodifférentiels à caractéristiques doubles et paramétrix associés. C. R. Acad. Sci. Paris (to appear)
[5] Gru?in, V. V.: On a class of hypoelliptic operators. Mat. Sbornik83, 456-473 (1970). Also in Math. USSR Sbornik12, 458-476 (1970)
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[7] Hörmander, L.: Pseudo-differential operators and non-elliptic boundary problems. Ann. of Math.83, 129-209 (1966) · Zbl 0132.07402 · doi:10.2307/1970473
[8] Hörmander, L.: Pseudo-differential operators and hypoelliptic equations. A.M.S. Proc. Symp. Pure Math.10, 138-183 (1967) · Zbl 0167.09603
[9] Ivrii, V. Ia., Petkov, V. M.: Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations. Usp. Mat. Nauk29, 3-70 (1974) · Zbl 0312.35049
[10] Melin, A.: Lower bounds for pseudo-differential operators. Ark. för Mat.9, 117-140 (1971) · Zbl 0211.17102 · doi:10.1007/BF02383640
[11] Radkevi?, E. V.: A priori estimates and hypoelliptic equations with multiple characteristics. Dokl. Akad. Nauk SSSR187, 274-277 (1969). Also in Soviet Math. Doklady10, 849-853 (1969)
[12] Segal, I. E.: Transforms for operators and symplectic automorphics over a locally compact abelian group. Math. Scand.13, 31-43 (1963) · Zbl 0208.39002
[13] Sjöstrand, J.: Parametrices for pseudodifferential operators with multiple characteristics. Ark. för Mat.12, 85-130 (1974) · Zbl 0317.35076 · doi:10.1007/BF02384749
[14] Weil, A.: Sur certains groupes d’opérateurs unitai res. Acta Math.111, 143-211 (1964) · Zbl 0203.03305 · doi:10.1007/BF02391012
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