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Loy, R. J.; Davies, Arthur Russell; Anderssen, R. S. (2009)
Publisher: Cambridge University Press
Languages: English
Types: Article
Subjects: QA
The duality proof of sampling localization given by Loy, Newbury, Anderssen and Davies in 2001 contains an oversight, as the classes of functions chosen do not assume the compact support. Here, it is shown how a minor change to the argument there yields a precise conclusion.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] A. R. Davies and R. S. Anderssen, 'Sampling localization in determining the relaxation spectra', J. Non-Newt. Fluid Mech. 73 (1997), 163-179.
    • [2] , 'Sampling localization and duality algorithms in practice', J. Non-Newt. Fluid Mech. 79 (1998), 235-253.
    • [3] A. Dienstfrey and L. Greengard, 'Analytic continuation, singular-value expansions, and KramersKronig analysis', Inverse Problems 17 (2001), 1307-1320.
    • [4] M. M. Lavrente┬┤v, Some Improperly Posed Problems of Mathematical Physics, Springer Tracts in Nat. Philos., II (Springer, New York, 1967).
    • [5] R. J. Loy, C. Newbury, R. S. Anderssen and A. R. Davies, 'A duality proof of sampling localization in relaxation spectrum recovery', Bull. Aust. Math. Soc. 64 (2001), 265-269.
    • [6] J. R. Macdonald, 'On relaxation-spectrum estimation for decades of data: accuracy and sampling localization considerations', Inverse Problems 16 (2000), 1561-1583.
    • [7] M. Renardy, 'On the use of Laplace transform inversion for reconstruction of relaxation spectra', J. Non-Newt. Fluid Mech. 154 (2008), 47-51. Available online at www.sciencedirect.com/science/journal/03770257
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