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Melrose, Richard B.

Transformation of boundary problems. (English) Zbl 0492.58023

Acta Math. 147, 149-236 (1981).
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Cited in 1 Review
Cited in 83 Documents

MSC:

58J32 Boundary value problems on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds
58J15 Relations of PDEs on manifolds with hyperfunctions
58J47 Propagation of singularities; initial value problems on manifolds

Keywords:

space of distributions supported on a manifold with boundary; compressed tangent and cotangent bundles; microlocalization with respect to pseudodifferential operators of totally characteristic type; Fourier integral operators on manifolds with boundary

Citations:

Zbl 0447.35053
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Full Text: DOI

References:

[1] Andersson, K. G. &Melrose, R. B., The propagation of singularities along gliding rays.Invent. Math., 41 (1977), 197–232. · Zbl 0373.35053 · doi:10.1007/BF01403048
[2] Boutet de Monvel, L., Opérateurs pseudo différentiels analytiques et problèmes aux limites elliptiques.Ann. Inst. Fourier, 19 (1969), 163–268. · Zbl 0176.08703
[3] –, Boundary value problems for pseudodifferential operators.Acta Math., 126 (1971), 11–51. · Zbl 0206.39401 · doi:10.1007/BF02392024
[4] Boutet de Monvel, L.,A course on pseudodifferential operators and their applications. Duke U. Math., Ser. 2, (1974). · Zbl 0294.35020
[5] Chazarain, J., Construction de la parametrix du problème mixte hyperbolique pour l’equation des ondes.C.R. Acad. Sci. Paris, 276 (1973), 1213–1215. · Zbl 0253.35058
[6] Duistermaat, J. J.,Fourier integral operators. Courant Institute lecture notes, 1973. · Zbl 0272.47028
[7] Guillemin, V. W. &Sternberg, S.,Geometric Asymptotics. Math. Surveys no. 14, A.M.S. Providence, 1977.
[8] Hörmander, L.,Linear partial differential operators. Springer, Berlin-Heidelberg-New York, 1963. · Zbl 0108.09301
[9] –, Pseudodifferential operators.Comm. Pure and Appl. Math., 18 (1965), 501–517. · Zbl 0125.33401 · doi:10.1002/cpa.3160180307
[10] –, Fourier integral operators I.Acta Math., 127 (1971), 79–183. · Zbl 0212.46601 · doi:10.1007/BF02392052
[11] Melrose, R. B., Microlocal parametrices for diffractive boundary value problems.Duke Math. J., 42 (1975), 605–635. · Zbl 0368.35055 · doi:10.1215/S0012-7094-75-04254-4
[12] Melrose, R. B., Parametrices at diffractive points. Unpublished (1975). · Zbl 0368.35055
[13] –, Differential boundary value problems of principal type. InSeminar on singularities of solutions of linear partial differential equations. Ed. L. Hörmander. Princeton Univ. Press, Princeton 1978.
[14] Melrose, R. B., Singularities of solutions to boundary value problems.Proc. Int. Congr. Math. Helsinki, 1978, pp. 785–790.
[15] Melrose, R. B., Transformation methods for boundary value problems. To appear inProc. Nato Adv. Study Meeting, Maratea 1980.
[16] Melrose, R. B. &Sjöstrand, J., Singularities of boundary value problems.Comm. Pure Appl. Math., 31 (1978), 593–617. · doi:10.1002/cpa.3160310504
[17] Peetre, J., Une caracterisation abstraite des operateurs differentiels; rectification.Math. Scand., 8 (1960), 116–120. · Zbl 0097.10402
[18] Robertson, A. P. & Robertson, W. J.,Topological vector spaces. Camb. Tracts in Mathematics 53, C.U.P. 1973. · Zbl 0251.46002
[19] Schwartz, L.,Theorie des distributions I, II. Paris, 1950. · Zbl 0037.07301
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