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Analytic wave front sets for solutions of linear differential equations of principal type. (English) Zbl 0259.35072


MSC:

35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A20 Analyticity in context of PDEs
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35S05 Pseudodifferential operators as generalizations of partial differential operators
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References:

[1] Karl Gustav Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat. 8 (1971), 277 – 302. · Zbl 0211.40502 · doi:10.1007/BF02589579
[2] Karl Gustav Andersson, Propagation of analyticity for solutions of differential equations of principal type, Bull. Amer. Math. Soc. 78 (1972), 479 – 482. · Zbl 0233.35003
[3] Louis Boutet de Monvel and Paul Krée, Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 1, 295 – 323 (English, with French summary). · Zbl 0195.14403
[4] A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations., Amer. J. Math. 80 (1958), 16 – 36. · Zbl 0080.30302 · doi:10.2307/2372819
[5] J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183 – 269. · Zbl 0232.47055 · doi:10.1007/BF02392165
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[7] Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79 – 183. · Zbl 0212.46601 · doi:10.1007/BF02392052
[8] Lars Hörmander, Linear differential operators, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 121 – 133. · Zbl 0223.35083
[9] Lars Hörmander, Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients, Comm. Pure Appl. Math. 24 (1971), 671 – 704. · Zbl 0226.35019 · doi:10.1002/cpa.3160240505
[10] Lars Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math. (2) 17 (1971), 99 – 163. · Zbl 0224.35084
[11] Takahiro Kawai, Construction of local elementary solutions for linear partial differential operators with real analytic coefficients. I. The case with real principal symbols, Publ. Res. Inst. Math. Sci. 7 (1971/72), 363 – 397. · Zbl 0216.12303 · doi:10.2977/prims/1195193547
[12] Bernard Malgrange, Travaux d’Écalle et de Martinet-Ramis sur les systèmes dynamiques, Bourbaki Seminar, Vol. 1981/1982, Astérisque, vol. 92, Soc. Math. France, Paris, 1982, pp. 59 – 73 (French).
[13] L. Nirenberg, Pseudo-differential operators, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 149 – 167.
[14] M. Sato, Hyperfunctions and partial differential equations, Proc. Internat. Conference on Functional Analysis and Related Topics (Tokyo, 1969), Univ. of Tokyo Press, Tokyo, 1970, pp. 91-94.
[15] Mikio Sato, Regularity of hyperfunctions solutions of partial differential equations, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 785 – 794.
[16] -, On pseudo-differential equations in hyper-function theory, Amer. Math. Soc. Sympos. on Partial Differential Equations, Berkeley, 1971.
[17] J. J. Duistermaat, On Carleman estimates for pseudo-differential operators, Invent. Math. 17 (1972), 31 – 43. · Zbl 0242.35069 · doi:10.1007/BF01390021
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