Advertisement

A Short Introduction to Boutet de Monvel’s Calculus

  • Elmar Schrohe
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 125)

Abstract

This paper provides an introduction to Boutet de Monvel’s calculus on the half-space R+ in the framework of a pseudodifferential calculus with operator-valued symbols.

Keywords

Pseudodifferential Operator Transmission Condition Short Introduction Symbol Class Boundary Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Boutet de Monvel. Boundary problems for pseudo-differential operators. Acta Math., 126:11–51, 1971.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    B. Gramsch. Relative Inversion in der Störungstheorie von Operatoren and W-Algebren. Math. Annalen 269:27–71, 1984.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    G. Grubb. Functional Calculus for Boundary Value Problems. Number 65 in Progress in Mathematics. Birkhäuser, Boston, Basel, second edition, 1996.Google Scholar
  4. 4.
    G. Grubb and L. Hörmander. The transmission property. Math. Scand., 67:273–289, 1990.MathSciNetzbMATHGoogle Scholar
  5. 5.
    T. Hirschmann. Functional analysis in cone and edge Sobolev spaces. Ann. Global Anal. Geom., 8:167–192, 1990.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    L. Hörmander. The Analysis of Linear Partial Differential Operators, volume I - IV. Springer-Verlag, Berlin, New York, Tokyo, 1983–1985.Google Scholar
  7. 7.
    H. Kumano-go. Pseudo-Differential Operators. The MIT Press,Cambridge, MA, and London, 1981.Google Scholar
  8. 8.
    S. Rempel and B.-W. Schulze. Index Theory of Elliptic Boundary Problems. Akademie-Verlag, Berlin, 1982.zbMATHGoogle Scholar
  9. 9.
    E. Schrohe. Fréchet algebras of pseudodifferential operators and boundary value problems. Birkhäuser Verlag. In preparation.Google Scholar
  10. 10.
    E. Schrohe. Boundedness and spectral invariance for standard pseudodifferential operators on anisotropically weighted LP Sobolev spaces. Integral Equations Operator Theory, 13:271–284, 1990.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    E. Schrohe. A characterization of the singular Green operators in Boutet de Monvel’s calculus via wedge Sobolev spaces. Comm. Partial Differential Equations, 19:677–699, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    E. Schrohe. A characterization of the uniform transmission property for pseudodifferential operators. In M. Demuth et al., editors, Pseudodifferential Operators and Mathematical Physics,Advances in Partial Differential Equations 1 pages 210–234. Akademie Verlag, Berlin, 1994.Google Scholar
  13. 13.
    E. Schrohe and B.-W. Schulze. Boundary value problems in Boutet de Monvel’s calculus for manifolds with conical singularities I. In M. Demuth et al., editors, Pseudodifferential Operators and Mathematical Physics,Advances in Partial Differential Equations 1, pages 97–209. Akademie Verlag, Berlin, 1994.Google Scholar
  14. 14.
    E. Schrohe and B.-W. Schulze. Boundary value problems in Boutet de Monvel’s calculus for manifolds with conical singularities II. In M. Demuth et al., editors, Boundary Value Problems, Schrödinger Operators, Deformation Quantization, Advances in Partial Differential Equations 2 pages 70–205. Akademie Verlag, Berlin, 1995.Google Scholar
  15. 15.
    E. Schrohe and B.-W. Schulze. Mellin operators in a pseudodifferential calculus for boundary value problems on manifolds with edges. Operator Theory: Advances Applications 102:255–285. 1998.MathSciNetGoogle Scholar
  16. 16.
    E. Schrohe and B.-W. Schulze. A symbol algebra for pseudodifferential boundary value problems for manifolds with edges. In M. Demuth et al., editors, Differential Equations,Asymptotic Analysis, and Mathematical Physics, volume 100 of Math. Research, pages 292–324, Berlin, 1997. Akademie Verlag.Google Scholar
  17. 17.
    E. Schrohe and B.-W. Schulze. Mellin and Green symbols for boundary value problems on manifolds with edges. Integral Equations Operator Theory, 34:339–363, 1999.MathSciNetzbMATHGoogle Scholar
  18. 18.
    E. Schrohe. Frèchet algebra techniques for boundary value problems on noncompact manifolds: Fredholm criteria and functional calculus via spectral invariance. Math. Nachr., 199:145–185, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    B.-W. Schulze. Pseudodifferential Operators on Manifolds with Singularities. North-Holland, Amsterdam, 1991.Google Scholar
  20. 20.
    J. Seiler. Continuity of edge and corner pseudo-differential operators. Math. Nachr., 205:163–182, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    M.I. Visik and G.I. Eskin. Normally solvable problems for elliptic systems in equations of convolution. Mat. Sb., 3:303–332, 1967.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Elmar Schrohe
    • 1
  1. 1.Institut Für MathematikUniversität PotsdamPotsdamGermany

Personalised recommendations