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Mellin Quantization in the Cone Calculus for Boutet de Monvel’s Algebra

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Book cover Partial Differential Operators and Mathematical Physics

Part of the book series: Operator Theory Advances and Applications ((OT,volume 78))

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Abstract

We present a pseudodifferential calculus for boundary value problems on manifolds with conical singularities. We then show how to associate to each totally characteristic (Fuchs type) pseudodifferential symbol with values in Boutet de Monvel’s algebra an operator-valued Mellin symbol is such a way that the difference between the two corresponding operators is smoothing in the interior. This allows us to extend the action of the operators to weighted Mellin-Sobolev spaces.

AMS Subject Classification: 35 S 15, 58 G 20, 46 E 35, 46 H 35.

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Authors and Affiliations

  1. Max-Planck-Arbeitsgruppe “Partielle Differentialgleichungen and Komplexe Analysis”, Universität Potsdam, 14415, Potsdam, Germany

    Elmar Schrohe & B.-W. Schulze

Authors
  1. Elmar Schrohe
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  2. B.-W. Schulze
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, Erzstrasse 1, 38678, Clausthal-Zellerfeld, Germany

    Michael Demuth

  2. Institut für Mathematik, Max Planck-Arbeitsgruppe “Partielle Differentialgleichungen and Komplexe Analysis” Universität Potsdam, Postfach 60 15 53, 14415, Potsdam, Germany

    Bert-Wolfgang Schulze

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Schrohe, E., Schulze, BW. (1995). Mellin Quantization in the Cone Calculus for Boutet de Monvel’s Algebra. In: Demuth, M., Schulze, BW. (eds) Partial Differential Operators and Mathematical Physics. Operator Theory Advances and Applications, vol 78. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9092-2_34

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  • DOI: https://doi.org/10.1007/978-3-0348-9092-2_34

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9903-1

  • Online ISBN: 978-3-0348-9092-2

  • eBook Packages: Springer Book Archive

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