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The Poisson summation formula for manifolds with boundary. (English) Zbl 0421.35082


MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
58J40 Pseudodifferential and Fourier integral operators on manifolds
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References:

[1] Andersson, K.; Melrose, R., The propagation of singularities along gliding rays, Invent. Math., 41, 23-95 (1977) · Zbl 0358.35048
[2] Chazarain, J., Construction de la paramétrix du problème mixte hyperbolique pour l’équation des ondes, C. R. Acad. Sci. Paris Sér. A.-B., 276, 1213-1215 (1973) · Zbl 0253.35058
[3] Chazarain, J., Formule de Poisson pour les variétés riemanniennes, Invent. Math., 24, 65-82 (1974) · Zbl 0281.35028
[4] Duistermaat, J. J.; Guillemin, V., The spectrum of positive elliptic operators and periodic geodesics, Invent. Math., 29, 39-79 (1975) · Zbl 0307.35071
[5] Duistermaat, J. J.; Hörmander, L., Fourier integral operators, II, Acta Math., 128, 183-269 (1972) · Zbl 0232.47055
[6] Hörmander, L., Fourier integral operators, I, Acta Math., 127, 79-183 (1971) · Zbl 0212.46601
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