Advertisement

Edge-Degenerate Families of Pseudo-Differential Operators on an Infinite Cylinder

  • J. Abed
  • B.-W. Schulze
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 205)

Abstract

We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.

Keywords

Edge-degenerate operators parameter-dependent pseudo-differential operators norm estimates with respect to a parameter 

Mathematics Subject Classification (2000)

Primary 35S35 Secondary 35J70 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Abed and B.-W. Schulze, Operators with corner-degenerate symbols, in New Developments in Pseudo-Differential Operators, Operator Theory: Advances and Applications, 189, Birkhäuser, 2009, 67–106.Google Scholar
  2. [2]
    D. Calvo, C.-I. Martin and B.-W. Schulze, Symbolic structures on corner manifolds, in Microlocal Analysis and Asymptotic Analysis, Keio University, Tokyo, 2005, 22–35.Google Scholar
  3. [3]
    D. Calvo and B.-W. Schulze, Operators on corner manifolds with exits to infinity, J. Differential Equations 19(2) (2006), 147–192.zbMATHMathSciNetGoogle Scholar
  4. [4]
    D. Calvo and B.-W. Schulze, Edge symbolic structure of second generation, Math. Nachr. 282(3) (2009), 348–367.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    H. O. Cordes, A Global Parametrix for Pseudo-Differential Operators overn, with Applications, Reprint, SFB 72, Universität Bonn, 1976.Google Scholar
  6. [6]
    G. Harutyunyan and B.-W. Schulze, Elliptic Mixed, Transmission and Singular Crack Problems, European Mathematical Society, 2008.Google Scholar
  7. [7]
    H. Kumano-go, Pseudo-Differential Operators, MIT, 1981.Google Scholar
  8. [8]
    L. Maniccia and B.-W. Schulze, An algebra of meromorphic corner symbols, Bull. Sciences Math. 127(1) (2003), 55–99.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    C. Parenti, Operatori pseudo-differenziali in ℝn e applicazioni, Annali Mat. Pura Appl. 93(4) (1972), 359–389.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    S. Rempel and B.-W. Schulze, Asymptotics for Elliptic Mixed Boundary Value Problems, Math. Research 50, Akademie-Verlag, 1989.Google Scholar
  11. [11]
    B.-W. Schulze, Boundary Value Problems and Singular Pseudo-Differential Operators, Wiley, 1998.Google Scholar
  12. [12]
    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, Operator Theory: Advances and Applications, Birkhäuser, 2001, 167–207.Google Scholar
  13. [13]
    B.-W. Schulze, Operators with symbol hierarchies and iterated asymptotics, Publ. Res. Inst. Math. Sci. 38(4) (2002), 735–802.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    M. A. Shubin, Pseudodifferential operators inn, Dokl. Akad. Nauk. SSSR 196 (1971), 316–319.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • J. Abed
    • 1
  • B.-W. Schulze
    • 1
  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany

Personalised recommendations