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Abstract and Applied Analysis
Volume 2008, Article ID 459310, 13 pages
http://dx.doi.org/10.1155/2008/459310
Research Article

Noncoherence of a Causal Wiener Algebra Used in Control Theory

Mathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, UK

Received 18 March 2008; Accepted 13 June 2008

Academic Editor: Ülle Kotta

Copyright © 2008 Amol Sasane. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Glaz, Commutative Coherent Rings, vol. 1371 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1989. View at MathSciNet
  2. W. S. McVoy and L. A. Rubel, β€œCoherence of some rings of functions,” Journal of Functional Analysis, vol. 21, no. 1, pp. 76–87, 1976. View at Google Scholar Β· View at MathSciNet
  3. R. Mortini and M. von Renteln, β€œIdeals in the Wiener algebra W+,” Journal of the Australian Mathematical Society. Series A, vol. 46, no. 2, pp. 220–228, 1989. View at Google Scholar Β· View at MathSciNet
  4. F. M. Callier and C. A. Desoer, β€œAn algebra of transfer functions for distributed linear time-invariant systems,” IEEE Transactions on Circuits and Systems, vol. 25, no. 9, pp. 651–662, 1978. View at Google Scholar Β· View at MathSciNet
  5. M. Vidyasagar, Control System Synthesis: A Factorization Approach, vol. 7 of MIT Press Series in Signal Processing, Optimization, and Control, MIT Press, Cambridge, Mass, USA, 1985. View at MathSciNet
  6. A. Quadrat, β€œAn introduction to internal stabilization of linear infinite dimensional systems,” Course Notes, École Internationale d'Automatique de Lille (02-06/09/02): Contrôle de systèmes à paramètres répartis: Théorie et Applications, 2002, http://www-sop.inria.fr/cafe/Alban.Quadrat/Pubs/Germany2.pdf. View at MathSciNet
  7. A. Quadrat, β€œThe fractional representation approach to synthesis problems: an algebraic analysis viewpoint. I. (Weakly) doubly coprime factorizations,” SIAM Journal on Control and Optimization, vol. 42, no. 1, pp. 266–299, 2003. View at Google Scholar Β· View at MathSciNet
  8. R. S. Strichartz, A Guide to Distribution Theory and Fourier Transforms, World Scientific, River Edge, NJ, USA, 2003. View at MathSciNet
  9. A. Browder, Introduction to Function Algebras, W. A. Benjamin, New York, NY, USA, 1969. View at MathSciNet
  10. V. P. Havin, S. V. Hruščëv, and N. K. Nikol'skiĭ, Eds., Linear and Complex Analysis Problem Book, V. P. Havin, S. V. Hruščëv, and N. K. Nikol'skiĭ, Eds., vol. 1043 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1984. View at MathSciNet
  11. H. Matsumura, Commutative Ring Theory, vol. 8 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1989. View at MathSciNet
  12. A. Quadrat, β€œOn a generalization of the Youla-Kučera parametrization. I. The fractional ideal approach to SISO systems,” Systems & Control Letters, vol. 50, no. 2, pp. 135–148, 2003. View at Google Scholar Β· View at MathSciNet