Rodino, Luigi; Zanghirati, Luisa Pseudo-differential operators with multiple characteristics and Gevrey singularities. (English) Zbl 0597.58034 Commun. Partial Differ. Equations 11, 673-711 (1986). Let A be an analytic pseudo-differential operator whose principal symbol is assumed to vanish exactly at the order \(k\geq 2\) on a regular submanifold of codimension 1 in the cotangent space. Let \(0<p<1\). Then under an appropriate p-Levi condition the authors prove a result of propagation of singularities in the Gevrey class \(G^ s\) with \(1<s<1/p\), construct null solutions with prescribed singularities and give a microlocal existence theorem. Reviewer: C.Zuily Cited in 1 ReviewCited in 9 Documents MSC: 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J47 Propagation of singularities; initial value problems on manifolds Keywords:pseudo-differential operator; propagation of singularities in the Gevrey class × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aoki T, I, II, III, IV, V, Proc. Japan. Acad., Ser. A 58 pp 58– (1982) · Zbl 0507.58039 · doi:10.3792/pjaa.58.58 [2] Bony J.M., Astérisque 34 pp 43– (1976) [3] DOI: 10.5802/aif.601 · Zbl 0312.35064 · doi:10.5802/aif.601 [4] DOI: 10.5802/aif.429 · Zbl 0235.47029 · doi:10.5802/aif.429 [5] DOI: 10.5802/aif.258 · Zbl 0195.14403 · doi:10.5802/aif.258 [6] Cattabriga L., Applications to the Cauchy problem for hyperbolic operators. pp 2– (1985) · Zbl 0581.35007 [7] Chazarain I.J., Ann. Inst. Fourier, Grenoble 24 pp 209– (1974) [8] DOI: 10.1007/BF02392165 · Zbl 0232.47055 · doi:10.1007/BF02392165 [9] Egorov J.V., Dokl. Akad. Nauk. SSSR 234 pp 280– (1977) [10] DOI: 10.1080/03605308308820303 · Zbl 0525.35086 · doi:10.1080/03605308308820303 [11] DOI: 10.1002/cpa.3160240505 · Zbl 0226.35019 · doi:10.1002/cpa.3160240505 [12] Hörmander. 1983. ”The analysis of linear partial differential operators, I, II”. Berlin, Heidelberg: Springer-Verlag. New York, Tokyo [13] Ivrii V. Ja., Sib. Mat. Zh. 17 pp 547– (1976) [14] Kessab, A. 1984. Propagation des singularités Gevrey pour des opérateurs à caractéristiques involutives\(title: Th\`ese, Universit\'e de Paris-Sud, Centre d'Orsay. 1984.\) [15] Komatsu H., J. Fac. Sci. Univ. Tokoyo, Sect 20 pp 25– (1973) [16] Liess, O. and Rodino, L. A general class of Gevrey type pseudodifferential operators. Journées Equations aux derivées partielles conf. n. 6. 1983. Saint-Jean-de-Monts. [17] Liess O., Boll. Un. Mat. It., Sez. VI 3 pp 233– (1984) [18] Mizohata S., J. Vaillant, Université de Paris VI pp 106– (1983) [19] DOI: 10.5802/aif.602 · Zbl 0313.58021 · doi:10.5802/aif.602 [20] DOI: 10.2977/prims/1195181409 · Zbl 0574.35082 · doi:10.2977/prims/1195181409 [21] Trèves F., I, Plenum Publ. Corp. (1980) [22] Wakabayashi S., Japan. J. Math. 6 pp 179– (1980) [23] DOI: 10.3792/pjaa.59.182 · Zbl 0527.35048 · doi:10.3792/pjaa.59.182 [24] Zanghirati L., Pseudodifferential operators of infinite order and Gevrey classes, Ann. Univ. Ferrara, to appear. · Zbl 0601.35110 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.