Colin de Verdière, Yves Spectre conjoint d’opérateurs pseudo-différentiels qui commutent. II. Le cas intégrable. (French) Zbl 0478.35073 Math. Z. 171, 51-73 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 50 Documents MSC: 35P05 General topics in linear spectral theory for PDEs 47F05 General theory of partial differential operators 35S05 Pseudodifferential operators as generalizations of partial differential operators 47D99 Groups and semigroups of linear operators, their generalizations and applications Keywords:Maslov index; joint spectrum; first-order selfadjoint commuting pseudodifferential operators; subprincipal symbols Citations:Zbl 0411.35073 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Bredon, G.: Introduction to compact transformation groups. New York-London: Academic Press 1972 · Zbl 0246.57017 [2] Bernstein, D.N.: The number of integral points in integral polyhedra. Functional Anal. Appl.10, 223-224 (1976) · Zbl 0347.52003 · doi:10.1007/BF01075529 [3] Courant, R., Hilbert, D.: Methods of mathematical physics, vol. 1. New York: Interscience 1953 · Zbl 0051.28802 [4] Colin de Verdière, Y., Vey, J.: Le lemme de Morse isochore. Topology18, 283-293 (1979) · Zbl 0441.58003 · doi:10.1016/0040-9383(79)90019-3 [5] Colin de Verdière, Y.: Quasi-modes sur les variétés riemanniennes compactes. Invent. Math.43, 15-52 (1977) · Zbl 0449.53040 · doi:10.1007/BF01390202 [6] Colin de Verdiere, Y.: Nombre de points entiers dans une famille homothétique de domaines de ? n . Ann. Sci. École Norm. Sup. 4e série,10, 559-576 (1977) [7] Colin de Verdiére, Y.: Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques. C.R. Acad. Paris Ser. A,286, 1195-1197, 1978 et Comment. Math. Hev.54, 508-522 (1979) · Zbl 0397.35054 [8] Colin de Verdière, Y.: Spectre conjoint d’opérateurs pseudo-différentiels qui commutent, I?Le cas non intégrable. Duke Math. J.46, 169-182 (1979) · Zbl 0411.35073 · doi:10.1215/S0012-7094-79-04608-8 [9] Duistermaaat, J.J.: Oscillatory integrals, Lagrange Immersions and Unfolding of Singularities. Comm. Pure Appl. Math.27, 207-281 (1974) · Zbl 0285.35010 · doi:10.1002/cpa.3160270205 [10] Duistermaat, J.J., Guillemin, V.: Spectrum of elliptic operators and periodic geodesics. Invent. Math.29, 39-79 (1975) · Zbl 0307.35071 · doi:10.1007/BF01405172 [11] Duistermaat, J.J., Hörmander, L.: Fourier integral operators II. Acta Math.128, 183-269 (1972) · Zbl 0232.47055 · doi:10.1007/BF02392165 [12] Guillemin, V.: Some spectral results on rank one symmetric space. Advances in Math.28, 129-137 (1978) · Zbl 0441.58012 · doi:10.1016/0001-8708(78)90059-2 [13] Hörmander, L.: The spectral function of an elliptic operator. Acta Math.121, 193-218 (1968) · Zbl 0164.13201 · doi:10.1007/BF02391913 [14] Hörmander, L.: Fourier integral operators I. Acta Math.127, 79-183 (1971) · Zbl 0212.46601 · doi:10.1007/BF02392052 [15] Helgason, S.: Differential geometry and symmetric spaces. New York-London: Academic Press 1962 · Zbl 0111.18101 [16] Hirschowitz, A.: Transmission et symbole sous-principal. C.R. Acad. Sci. Paris Sér A.285, 1069-1071 (1977) · Zbl 0379.35061 [17] Hirschowitz, A., Piriou, A.: Propriétés de transmission pour les distributions intégrales de Fourier, Preprint Université de Nice · Zbl 0456.58028 [18] Maslov, V.P.: Théorie des perturbations et méthodes asymptotiques. Paris: Dunod 1972 [19] Mac-Mullen, P.: Metrical and combinatorial properties of convex polytopes. In: Proceedings of the International Congress of Mathematicians (Vancouver 1974), pp. 491-494. Vancouver: Canadian Mathematical Congress 1975 [20] Strichartz, A.: A functional calculus for pseudo-differential operators. Amer. J. Math.94, 711-712 (1972) · Zbl 0246.35082 · doi:10.2307/2373753 [21] Vey, J.: Sur le lemme de Morse. Invent. Math.40, 1-10 (1977) · Zbl 0348.58007 · doi:10.1007/BF01389858 [22] Vey, J.: Sur certains systèmes dynamiques séparables. Amer. J. Math.100, 591-614 (1978) · Zbl 0384.58012 · doi:10.2307/2373841 [23] Voros, A.: The WKB method for non separable systems. In: Colloques internationaux du C.N.R.S.237. Géometrie Symplectique et Physique Mathématique (Aix 1974), pp. 277-287. Paris: Editions du C.N.R.S. 1975 [24] Weinstein, A.: Fourier integral operators, quantization and the spectra of riemannian manifolds. In: Colloque internationaux du C.N.R.S.237. Géometrie Sympectique et Physique Mathématique (Aix 1974), pp. 289-298. Paris: Editions du C.N.R.S. 1975 [25] Weinstein, A.: Symplectic manifolds and their lagrangien submanifolds. Advances in Math.6, 329-346 (1971) · Zbl 0213.48203 · doi:10.1016/0001-8708(71)90020-X [26] Weinstein, A.: On Maslov’s quantization conditions. In: Fourier Integral Operators Colloque International (Nice 1974), pp. 341-372. Lecture Notes in Mathematics459. Berlin-Heidelberg-New York: Springer 1975 [27] Weinstein, A.: Asymptotics of the eigenvalues clusters for the laplacian plus a potential. Duke Math. J.44, 883-892 (1977) · Zbl 0385.58013 · doi:10.1215/S0012-7094-77-04442-8 [28] Weil, A.: L’intégration dans les groupes topologiques et ses applications (2e édition). Paris: Hermann 1965 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.