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Spectral Invariance of Pseudodifferential Boundary Value Problems on Manifolds with Conical Singularities

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Abstract

We prove the spectral invariance of the algebra of classical pseudodifferential boundary value problems on manifolds with conical singularities in the \(L_{p}\)-setting. As a consequence we also obtain the spectral invariance of the classical Boutet de Monvel algebra of zero order operators with parameters. In order to establish these results, we show the equivalence of Fredholm property and ellipticity for both cases.

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Notes

  1. The result is stated for \(s=0\) but extends to other values of s.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090, São Paulo, SP, Brazil

    Pedro T. P. Lopes

  2. Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Elmar Schrohe

Authors
  1. Pedro T. P. Lopes
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  2. Elmar Schrohe
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Correspondence to Pedro T. P. Lopes.

Additional information

Communicated by Michael Ruzhansky.

Pedro T. P. Lopes was partially supported by FAPESP (Processo Número 2016/07016-8).

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Lopes, P.T.P., Schrohe, E. Spectral Invariance of Pseudodifferential Boundary Value Problems on Manifolds with Conical Singularities. J Fourier Anal Appl 25, 1147–1202 (2019). https://doi.org/10.1007/s00041-018-9607-5

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  • DOI: https://doi.org/10.1007/s00041-018-9607-5

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