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Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics

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References

  1. Agranovič, M.S., Višik, M.I., Elliptic problems with parameter and parabolic problems of general type. Uspehi Nat. Nauk19,3(1964) 53–161 (Russ. Math. Survey19,3(1964) 53–159).

    Google Scholar 

  2. Baouendi, M.S., Sjöstrand, J., Régularité analytique pour des opérateurs elliptiques singuliers en un point, Arkiv för Mat.14(1976) 9–33.

    Google Scholar 

  3. Baouendi, M.S., Sjöstrand, J., Analytic regularity for the Dirichlet problem in domains with conic singularities. Annali Sc. Normale Superiore Pisa, Ser. IV, Vol. IV, no. 3 (1977) 515–530.

    Google Scholar 

  4. Bolley, P., Camus, J., Helffer, B., Sur une classe d'opérateurs partiellement hypoelliptiques. J. math. pures appl.55(1976) 131–171.

    Google Scholar 

  5. Brüning, J., Seeley, R., Regular singular asymptotics, Preprint, University of Massachusetts

  6. Cheeger, J., Spectral geometry of spaces with cone-like sigularities. Proc.Nat.Acad.Sci. USA76(1979) 2103–2106.

    Google Scholar 

  7. Cheeger, J., Taylor, M., On the diffraction of waves by conical singularities I. Comm. Pure Appl. Math.35 (1982) 275–331, II. Comm. Pure Appl. Math.35 (1982) 487–530.

    Google Scholar 

  8. Elschner, J., Singular ordinary differential operators and pseudodifferential equations. Mathematics Research Series, Akademie-Verlag Berlin 1985.

    Google Scholar 

  9. Kondrat'ev, V.A., Boundary value problems for elliptic equations in domain with conical points. Trudy Mosk.Mat.Obšč.16 (1967)209–292 (Transactions Moscow Math. Soc. (1967) 227–313).

    Google Scholar 

  10. Kondrat'ev, V.A., Olejnik, O.A., Boundary problems for partial differential equations in non-smooth domains. Uspehi Mat. Nauk38, 2 (1983) 3–76.

    Google Scholar 

  11. Lewis, J.E., Parenti, C., Pseudodifferential operators of Mellin type. Comm. Part. Diff. Equ.85 (1983) 477–544.

    Google Scholar 

  12. Melrose, R., Transformation of boundary problems. Acta Math. 147 (1981) 149–236.

    Google Scholar 

  13. Melrose, R., Mendoza, G.A., Elliptic boundary problems in spaces with conical points. Journees “Equ.Deriv.part.” St. Jean de Monts 1981, Conf. 4.

  14. —, Elliptic operators of totally characteristic type, Math. Sc. Res. Inst. Preprint MSRI 047–83

  15. Müller, W., Spectral theory for Riemannian manifolds with cusps and a related trace formula, Report IMath 1982.

  16. Pham The Lai, Problème de Dirichlet dans un cone avec parametre spectral pour une classe d'espaces de Sobolev a poids. Comm. Part.Diff. Equ.4, 4 (1979) 389–445.

    Google Scholar 

  17. Plamenevskii, B.A., An algebra of pseudo-differential operators in spaces with weight. Mat.Sb.106, 2 (1978) 297–320 (Math. USSR Sbornik 24 (1978) 841–865).

    Google Scholar 

  18. Rempel, S., Schulze, B.-W., Parametrices and boundary symbolic calculus for elliptic boundary problems without the transmission property.Math. Nachr.105 (1982) 45–149.

    Google Scholar 

  19. —, Pseudo-differential and Mellin operators in spaces with conormal singularity (boundary symbols). IMath Report Berlin 1984.

  20. —, Asymptotics for elliptic mixed boundary problems (Pseudo-differential and Mellin operators in spaces with conormal singularity). Mathematics Research Series, Akademie-Verlag Berlin (to appear 1986).

  21. —, Mellin symbolic calculus and asymptotics for boundary value problems. Seminar Analysis 1984/85 des Karl-Weierstraβ-Instituts für Mathematik, Berlin 1985

  22. —, Complete Mellin symbols and the conormal asymptotics in boundary value problems. Proc. Journees “Equations aux Deriv. Part.” St.-Jean- de Monts 1984, Conf. N° V.

  23. —, Branching of asymptotics for elliptic operators on manifolds with wedges. Partial Diff. Equ., Banach Center Publ. (to appear in Proc. of the Semester 1984, vol.19)

  24. Šubin, M.A., Pseudodifferential operators and spectral theory, Nauka, Moscow 1978.

    Google Scholar 

  25. Treves, F., Topological vector spaces, distributions and kernels. Academic Press New York, London 1967.

    Google Scholar 

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Rempel, S., Schulze, BW. Complete Mellin and Green symbolic calculus in spaces with conormal asymptotics. Ann Glob Anal Geom 4, 137–223 (1986). https://doi.org/10.1007/BF00129908

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