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4.4 Comments and References
T. Arens: Uniqueness for Elastic Wave Scattering by Rough Surfaces, SIAM J. Math. Anal. 33 (2001), 461–476.
T. Arens: Existence of Solution in Elastic Wave Scattering by Unbounded Rough Surfaces, Math. Meth. Appl. Sci. 25 (2002), 507–528.
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.
S. N. Chandler-Wilde and M. Lindner: Boundary integral equations on unbounded rough surfaces: Fredholmness and the Finite Section Method, submitted for publication (2006).
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.
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.
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.
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.
M. Lindner and B. Silbermann: Finite Sections in an Algebra of Convolution and Multiplication Operators on L∞(ℝ), TU Chemnitz, Preprint 6 (2000).
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.
M. Lindner: Limit Operators and Applications on the Space of essentially bounded Functions, Dissertation, TU Chemnitz 2003.
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.
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.
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.
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.
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).
S. Roch: Band-dominated operators on ℓ p spaces: Fredholm indices and finite sections, Acta Sci. Math. 70 (2004), no. 3–4, 783–797.
S. Roch: Finite sections of band-dominated operators, Preprint Nr. 2355, Technical University Darmstadt, 2004 (to appear in Memoirs AMS, 2006).
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(2006). Stability of the Finite Section Method. In: Infinite Matrices and their Finite Sections. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7767-0_4
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