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Operators with Corner-Degenerate Symbols

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New Developments in Pseudo-Differential Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 189))

Abstract

We establish elements of a new approach to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level.

The“full” calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near a corner point.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Neuen Palais 10, D-14469, Potsdam, Germany

    Jamil Abed & Bert-Wolfgang Schulze

Authors
  1. Jamil Abed
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  2. Bert-Wolfgang Schulze
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Universitá di Torino, Via Carlo Alberto, 10, 10123, Torino, Italy

    Luigi Rodino

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada

    M. W. Wong

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Abed, J., Schulze, BW. (2008). Operators with Corner-Degenerate Symbols. In: Rodino, L., Wong, M.W. (eds) New Developments in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 189. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8969-7_5

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