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The Quantization of Edge Symbols

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Modern Trends in Pseudo-Differential Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 172))

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Abstract

We investigate operators on manifolds with edges from the point of view of the symbolic calculus induced by the singularities. We discuss new aspects of the quantization of edge-degenerate symbols which lead to continuous operators in weighted edge spaces.

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References

  1. D. Calvo and B.-W. Schulze, Operators on corner manifolds with exits to infinity, Journal of Differential Equ. 19,2 (2006), 147–192.

    MATH  MathSciNet  Google Scholar 

  2. D. Calvo, C.-I. Martin and B.-W. Schulze, Symbolic structures on corner manifolds, in RIMS Conference on Microlocal Analysis and Asymptotic Analysis, Keio University, Tokyo, 2005, 22–35.

    Google Scholar 

  3. D. Calvo and B.-W. Schulze, Edge calculus of second generation, Preprint, Institut für Mathematik, Universität Potsdam, 2005.

    Google Scholar 

  4. N. Dines and B.-W. Schulze, Mellin-edge-representations of elliptic operators, Math. Meth. Appl. Sci. 28 (2005), 2133–2172.

    Article  MATH  MathSciNet  Google Scholar 

  5. J.B. Gil, B.-W. Schulze and J. Seiler, Cone pseudodifferential operators in the edge symbolic calculus, Osaka J. Math. 37 (2000), 219–258.

    MathSciNet  Google Scholar 

  6. G. Harutjunjan and B.-W. Schulze, The relative index for corner singularities, Integral Equations Operator Theory 54,3 (2006), 385–426.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Harutjunjan and B.-W. Schulze, Elliptic Mixed, Transmission and Singular Crack Problems, European Mathematical Soc., Zürich, 2007, to appear.

    Google Scholar 

  8. T. Hirschmann, Functional analysis in cone and edge Sobolev spaces, Ann. Global Anal. Geom. 8 (1990), 167–192.

    Article  MATH  MathSciNet  Google Scholar 

  9. I.L. Hwang, The L 2-boundness of pseudodifferential operators, Trans. Amer. Math. Soc. 302 (1987), 55–76.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Kapanadze and B.-W. Schulze, Crack Theory and Edge Singularities, Kluwer Academic Publ., Dordrecht, 2003.

    MATH  Google Scholar 

  11. L. Maniccia and B.-W. Schulze, An algebra of meromorphic corner symbols, Bull. des Sciences Math. 127 (2003), 55–99.

    Article  MATH  MathSciNet  Google Scholar 

  12. B.-W. Schulze, Pseudo-differential operators on manifolds with edges, in Partial Differential Equations, Teubner, Teubner-Texte zur Mathematik, Leipzig, 1989, 259–287.

    Google Scholar 

  13. B.-W. Schulze, Pseudo-differential Operators on Manifolds with Singularities, North-Holland, Amsterdam, 1991.

    MATH  Google Scholar 

  14. B.-W. Schulze, Corner Mellin operators and conormal asymptotics, in Sem. Equ. aux Dériv. Part. 1990–1991, Exp. XII, Ecole Polytechnique, Mars 1991.

    Google Scholar 

  15. B.-W. Schulze, Boundary Value Problems and Singular Pseudo-differential Operators. J. Wiley, Chichester, 1998.

    MATH  Google Scholar 

  16. B.-W. Schulze, Operator algebras with symbol hierarchies on manifolds with singularities, in Advances in Partial Differential Equations (Approaches to Singular Analysis), Editors: J. Gil, D. Grieser and M. Lesch, Birkhäuser, Basel, 2001, 167–207.

    Google Scholar 

  17. B.-W. Schulze, Operators with symbol hierarchies and iterated asymptotics, Publ. RIMS, Kyoto University 38 (2002), 735–802.

    MATH  MathSciNet  Google Scholar 

  18. B.-W. Schulze and J. Seiler, The edge algebra structure of boundary value problems, Ann. Global Anal. and Geom. 22 (2002), 197–265.

    Article  MATH  MathSciNet  Google Scholar 

  19. B.-W. Schulze and N. Tarkhanov, New algebras of boundary value problems for elliptic pseudodifferential operators. Preprint, Institut für Mathematik, Universität Potsdam, 2005.

    Google Scholar 

  20. B.-W. Schulze and A. Volpato, Green operators in the edge Quantisation of elliptic operators. Preprint, Institut für Mathematik, Universität Potsdam, 2004.

    Google Scholar 

  21. J. Seiler, Continuity of edge and corner pseudodifferential operators. Math. Nachr., 205, (1999), 163–182.

    MATH  MathSciNet  Google Scholar 

  22. J. Seiler, The cone algebra and a kernel characterization of Green operators, in Advances in Partial Differential Equations (Approaches to Singular Analysis), Editors: J. Gil, D. Grieser and M. Lesch, Birkhäuser, Basel, 2001, 1–29.

    Google Scholar 

  23. N. Tarkhanov, Harmonic integrals on domains with edges, Preprint, Institut für Mathematik, Universität Potsdam, 2004.

    Google Scholar 

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Author information

Authors and Affiliations

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

    C. -I. Martin & B. -W. Schulze

Authors
  1. C. -I. Martin
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  2. B. -W. Schulze
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Editor information

Editors and Affiliations

  1. School of Mathematics and Systems Engineering, Växjö University, SE-351 95, Växjö, Sweden

    Joachim Toft

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Martin, C.I., Schulze, B.W. (2006). The Quantization of Edge Symbols. In: Toft, J. (eds) Modern Trends in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 172. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8116-5_1

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