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A Calculus of Abstract Edge Pseudodifferential Operators of Type \(\rho,\delta\)

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Book cover Elliptic and Parabolic Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 119))

Abstract

In this paper, we expand on B.-W. Schulze’s abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on Hörmander’s \(\rho,\delta\) calculus, where \(0 \leq \delta < \rho \leq 1\). This expansion is motivated by recent work on boundary value problems for elliptic wedge operators with variable indicial roots by G. Mendoza and the author, where operators of type \(1,\delta\) for \(0 < \delta < 1\) appear naturally. Some of the results of this chapter also represent improvements over the existing literature on the standard abstract edge calculus of operators of type 1,0, such as trace class mapping properties of operators in abstract wedge Sobolev spaces. The presentation in this paper is largely self-contained to allow for an independent reading.

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Acknowledgments

This material is based in part upon work supported by the National Science Foundation under Grant No. DMS-0901202.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Pennsylvania State University, 3000 Ivyside Park, Altoona Campus, Altoona, PA, 16601, USA

    Thomas Krainer

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  1. Thomas Krainer
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Correspondence to Thomas Krainer .

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Editors and Affiliations

  1. Institute for Applied Mathematics, Leibniz University of Hannover, Hannover, Germany

    Joachim Escher

  2. Institute for Analysis, Leibniz University of Hannover, Hannover, Germany

    Elmar Schrohe

  3. Department of Mathematics, University of Torino, Torino, Torino, Italy

    Jörg Seiler

  4. Institute for Applied Mathematics, Leibniz University of Hannover, Hannover, Germany

    Christoph Walker

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Krainer, T. (2015). A Calculus of Abstract Edge Pseudodifferential Operators of Type \(\rho,\delta\) . In: Escher, J., Schrohe, E., Seiler, J., Walker, C. (eds) Elliptic and Parabolic Equations. Springer Proceedings in Mathematics & Statistics, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-12547-3_8

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