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Étude spectrale d’opérateurs hypoelliptiques à caractéristiques multiples. I. (French) Zbl 0488.35079


MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
35P20 Asymptotic distributions of eigenvalues in context of PDEs
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References:

[1] S. AGMON, Lectures on elliptic boundary value problems, Van Nostrand, Math. Studies (1965).0142.3740131 #2504 · Zbl 0142.37401
[2] P. BOLLEY, J. CAMUS, PHAM THE LAI, Noyau, résolvante et valeurs propres d’une classe d’opérateurs elliptiques et dégénérés, Lectures Notes in Math., 660, Berlin, Springer (1978), 33-46.0389.3503681b:35078JEDP_1977____33_0 · Zbl 0389.35036
[3] L. BOUTET DE MONVEL, Hypoelliptic operators with double characteristics and related pseudo-differential operators, Comm. Pure Appl. Math., 27 (1974), 585-639.0294.3502051 #6498 · Zbl 0294.35020
[4] L. BOUTET DE MONVEL, F. TREVES, On a class of pseudo-differential operators with double characteristics, Inv. Math., 24 (1974), 1-34.0281.3508350 #5550 · Zbl 0281.35083
[5] L. BOUTET DE MONVEL, A. GRIGIS, B. HELFFER, Paramétrixes d’opérateurs pseudo-différentiels à caractéristiques multiples, Astérisque, 34-35 (1976), 93-121.0344.3200958 #12046JEDP_1975____93_0 · Zbl 0344.32009
[6] V.V. GRUSHIN, On the proof of the discretness of the spectrum of a class of pseudo-differential in Rn, Funct. Anal. Appl., 5 (1971), 58-59.0227.35074 · Zbl 0227.35074
[7] B. HELFFER, Invariants associés à une classe d’opérateurs pseudo-différentiels et applications à l’hypoellipticité, Ann. de l’Inst. Fourier, Grenoble, 26, 2 (1976), 55-70.0301.3502654 #1318AIF_1976__26_2_55_0 · Zbl 0301.35026
[8] B. HELFFER, Sur l’hypoellipticité des opérateurs pseudo-différentiels à caractéristiques multiples, Bull. Soc. Math. France, 51-52 (1977), 13-61.0374.35012MSMF_1977__51-52__13_0 · Zbl 0374.35012
[9] L. HÖRMANDER, Fourier integral operators I, Acta. Math., 127 (1971), 79-183.0212.4660152 #9299 · Zbl 0212.46601
[10] L. HÖRMANDER, The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math., 32 (1979), 359-443.0388.47032 · Zbl 0388.47032
[11] [11] , Neuer beweis and verallgemeinerung der Tauberschen sätze, welch die Laplacesche and Stieltjessche transformation betreffen, J. Reine u. Angew. Math., 164 (1931), 27-39. · JFM 57.0262.01
[12] R.B. MELROSE, Hypoelliptic operators with characteristic variety of codimension two and the wave equation, Seminaire Goulaouic-Schwartz, 1979-1980, Centre Math. Ecole polytechnique, Palaiseau, (1980).0468.35032SEDP_1979-1980____A12_0 · Zbl 0468.35032
[13] A. MENIKOFF, J. SJÖSTRAND, On the eigenvalues of a class of hypoelliptic operators, Math. Ann., 235 (1978), 55-85.0375.3501458 #1735 · Zbl 0375.35014
[14] A. MENIKOFF, J. SJÖSTRAND, On the eigenvalues of a class of hypoelliptic operators II, Lecture Notes in Math., 755, Berlin, Springer (1979), 201-247.0444.3501982m:35114 · Zbl 0444.35019
[15] [15] , , The eigenvalues of hypoelliptic operators III, the non semi-bounded case, J. Analyse Math., 35 (1979), 123-150. · Zbl 0436.35065
[16] [16] , Propriétés spectrales d’opérateurs pseudo-différentiels, Comm. in Partial Diff. Eq., 3 (1978), 755-826. · Zbl 0392.35056
[17] [17] , Parametrices for pseudo-differential operators with multiple characteristics, Ark. für Math., 12 (1974), 85-130. · Zbl 0317.35076
[18] J. SJÖSTRAND, Eigenvalues for hypoelliptic operators and related methods, Proc. Inter. Congress of Math. Helsinki, 1978, 445. · Zbl 0442.35029
[19] J. SJÖSTRAND, On the eigenvalues of a class of hypoelliptic operators IV, Ann. de l’Inst. Fourier, Grenoble, 30,2 (1980), 109-169.0417.4702482m:35116AIF_1980__30_2_109_0 · Zbl 0417.47024
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