Stability of the Finite Section Method

Part of the Frontiers in Mathematics book series (FM)


Section Method Integral Operator Multiplication Operator Banach Algebra Limit Operator 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

4.4 Comments and References

  1. [2]
    T. Arens: Uniqueness for Elastic Wave Scattering by Rough Surfaces, SIAM J. Math. Anal. 33 (2001), 461–476.MATHMathSciNetCrossRefGoogle Scholar
  2. [3]
    T. Arens: Existence of Solution in Elastic Wave Scattering by Unbounded Rough Surfaces, Math. Meth. Appl. Sci. 25 (2002), 507–528.MATHMathSciNetCrossRefGoogle Scholar
  3. [4]
    T. Arens, S. N. Chandler-Wilde and K. Haseloh: Solvability and spectral properties of integral equations on the real line. II. L p-spaces and applications, J. Integral Equations Appl. 15 (2003), no. 1, 1–35.MATHMathSciNetGoogle Scholar
  4. [18]
    S. N. Chandler-Wilde and M. Lindner: Boundary integral equations on unbounded rough surfaces: Fredholmness and the Finite Section Method, submitted for publication (2006).Google Scholar
  5. [19]
    S. N. Chandler-Wilde and A. Meier: On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering, Math. Methods Appl. Sci., 24 (2001), no. 4, 209–232.MATHMathSciNetCrossRefGoogle Scholar
  6. [21]
    S. N. Chandler-Wilde, C. R. Ross and B. Zhang: Scattering by infinite one-dimensional rough surfaces, Proc. R. Soc. Lond. A., 455 (1999), 3767–3787.MATHMathSciNetCrossRefGoogle Scholar
  7. [22]
    S. N. Chandler-Wilde and C. R. Ross: Scattering by rough surfaces: The Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane, Math. Meth. Appl. Sci., 19 (1996), 959–976.MATHMathSciNetCrossRefGoogle Scholar
  8. [23]
    S. N. Chandler-Wilde and B. Zhang: On the solvability of a class of second kind integral equations on unbounded domains, J. Math. Anal. Appl. 214 (1997), no. 2, 482–502.MATHMathSciNetCrossRefGoogle Scholar
  9. [46]
    M. Lindner and B. Silbermann: Finite Sections in an Algebra of Convolution and Multiplication Operators on L∞(ℝ), TU Chemnitz, Preprint 6 (2000).Google Scholar
  10. [48]
    M. Lindner: The finite section method in the space of essentially bounded functions: An approach using limit operators, Numer. Func. Anal. & Optim. 24 (2003) no. 7&8, 863–893.MATHMathSciNetCrossRefGoogle Scholar
  11. [50]
    M. Lindner: Limit Operators and Applications on the Space of essentially bounded Functions, Dissertation, TU Chemnitz 2003.Google Scholar
  12. [51]
    M. Lindner, V. S. Rabinovich and S. Roch: Finite sections of band operators with slowly oscilating coefficients, Linear Algebra and Applications 390 (2004), 19–26.MATHMathSciNetCrossRefGoogle Scholar
  13. [67]
    V. S. Rabinovich, S. Roch and B. Silbermann: Fredholm Theory and Finite Section Method for Band-dominated operators, Integral Equations Operator Theory 30 (1998), no. 4, 452–495.MATHMathSciNetCrossRefGoogle Scholar
  14. [68]
    V. S. Rabinovich, S. Roch and B. Silbermann: Band-dominated operators with operator-valued coefficients, their Fredholm properties and finite sections, Integral Equations Operator Theory 40 (2001), no. 3, 342–381.MATHMathSciNetCrossRefGoogle Scholar
  15. [69]
    V. S. Rabinovich, S. Roch and B. Silbermann: Algebras of approximation sequences: Finite sections of band-dominated operators, Acta Appl. Math. 65 (2001), 315–332.MATHMathSciNetCrossRefGoogle Scholar
  16. [71]
    V. S. Rabinovich, S. Roch and B. Silbermann: Finite Sections of band-dominated operators with almost periodic coefficients, Preprint Nr. 2398, Technical University Darmstadt, 2005 (to appear in Modern Operator Theory and Applications, 170, The Simonenko Anniversary Volume, Birkhäuser 2006).Google Scholar
  17. [74]
    S. Roch: Band-dominated operators on p spaces: Fredholm indices and finite sections, Acta Sci. Math. 70 (2004), no. 3–4, 783–797.MATHMathSciNetGoogle Scholar
  18. [75]
    S. Roch: Finite sections of band-dominated operators, Preprint Nr. 2355, Technical University Darmstadt, 2004 (to appear in Memoirs AMS, 2006).Google Scholar

Copyright information

© Birkhäuser Verlag 2006

Personalised recommendations