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Sjöstrand, Johannes

Parametrices for pseudodifferential operators with multiple characteristics. (English) Zbl 0317.35076

Ark. Mat. 12, 85-130 (1974).
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Cited in 8 Reviews
Cited in 94 Documents

MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
65H10 Numerical computation of solutions to systems of equations
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References:

[1] Boutet de Monvel, L. & Trèves, F.,On a class of pseudodifferential operators with double characteristics. Preprint, Rutgers University. · Zbl 0281.35083
[2] Cardoso, F. & Trèves, F.,Necessary conditions of local solvability for differential equations with double characteristics. Preprint, Princetons and Rutgers University. · Zbl 0273.35058
[3] Duistermaat, J. J.; Hörmander, L., Fourier integral operators II, Acta Math., 128, 183-269 (1972) · Zbl 0232.47055 · doi:10.1007/BF02392165
[4] Duistermaat, J. J.; Sjöstrand, J., A global construction for pseudodifferential operators with non-involutive characteristics, Invent. Math., 20, Fasc. 3, 209-225 (1973) · Zbl 0282.35071 · doi:10.1007/BF01394095
[5] Gilioli, A. & Trèves, F.An example in the local solvability theory of linear PDE’s. Preprint, Rutgers University. · Zbl 0308.35022
[6] Grušin, V. V., Pseudodifferentia operators onR^n with bounded symbols, Funkcional Anal. i Priložen., 4, no 4, 37-50 (1970) · Zbl 0223.35084
[7] Grušin, V. V., On the proof of the discreteness of the spectrum of one class of differential operators inR^n, Funkcional Anal. i. Priložen., 5, no 1, 71-72 (1971) · Zbl 0227.35074
[8] Grušin, V. V., On a class of hypoelliptic operators, Mat. Sb., 83, 125, 456-473 (1970) · Zbl 0211.40503
[9] Grušin, V. V., On a class of elliptic operators, degenerate on a submanifold, Mat. Sb., 84, 126, 163-195 (1971) · Zbl 0215.49203
[10] Grušin, V. V., Differential equations and pseudodifferential operators with operator valued symbols, Mat. Sb., 88, 130, 504-521 (1972) · Zbl 0243.35020
[11] Hörmander, L., Fourier integral operators I, Acta Math., 127, 79-183 (1971) · Zbl 0212.46601 · doi:10.1007/BF02392052
[12] Hörmander, L., Pseudodifferential operators and hypoelliptic equations, Amer. Math. Soc. Symp. Pure Math., 10, 138-183 (1966) · Zbl 0167.09603
[13] Hörmander, L., On the existence and the regularity of solutions of linear pseudodifferential equations, Enseignement Math., XVII, fasc 2, 99-163 (1971) · Zbl 0224.35084
[14] Hörmander, L.Linear partial differential operators. Grundlehren d. Math. Wiss. 116. Springer-Verlag, 1963. · Zbl 0108.09301
[15] Melin, A., Lower bounds for pseudodifferential operators, Ark. Mat., 9, 117-140 (1971) · Zbl 0211.17102 · doi:10.1007/BF02383640
[16] Mizohata, S.; Ohya, Y., Sur la condition de E. E. Levi concernant des équations hyperboliques, Publ. Res. Inst. Math. Sci. A, 4, 511-526 (1968) · Zbl 0202.37401 · doi:10.2977/prims/1195194888
[17] Moyer, R. D.,On the Nirenberg-Treves condition for local solvability. Unpublished manuscript, University of Kansas. · Zbl 0344.35002
[18] Nirenberg, L.; Trèves, F., On local solvability of linear partial differential equations, Part I and II, Comm. Pure Appl. math., 23, 1-38 (1970) · Zbl 0191.39103 · doi:10.1002/cpa.3160230102
[19] Radkevič, E. v., A priori estimates and hypoelliptic operators with multiple charateristics, Dokl. Akad. Nauk SSSR, 187, no 2, 274-277 (1969) · Zbl 0206.10403
[20] Radkevič, E. V., Hypoelliptic operators with multiple characteristics, Mat. Sb., 79, 121, 193-216 (1969) · Zbl 0207.09401
[21] Sjöstrand, J., Operators of principal type with interior boundary conditions, Acta Math., 130, 1-51 (1973) · Zbl 0253.35076 · doi:10.1007/BF02392261
[22] Sjöstrand, J., Une classe d’opérateurs pseudodifférentiels à caractéristiques multiples, C. R. Acad. Sci. Paris, 275, 817-819 (1972) · Zbl 0252.47052
[23] Sjöstrand, J., Une classe d’opérateurs pseudodifférentiels à caractéristiques doubles, C. R. Acad. Sci. Paris, 275, 743-745 (1973) · Zbl 0248.35107
[24] Trèves, F., A new method of proof of the subelliptic estimates, Comm. Pure Appl. Math., 24, 71-115 (1971) · Zbl 0206.11401 · doi:10.1002/cpa.3160240107
[25] Višik, M. I.; Grušin, V. V., Elliptic pseudodifferential operators on a closed manifold which degenerate on a submanifold, Dokl. Akad. Nauk SSSR, 189, no 1, 16-19 (1969) · Zbl 0238.35078
[26] Višik, M. I.; Grušin, V. V., On a class of higher order degenerate elliptic equations, Mat. Sb., 79, 121, 3-36 (1969) · Zbl 0177.14302
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