Direct form seminorms arising in the theory of interpolation by translates of a basis function |
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Authors: | Jeremy Levesley Will Light |
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Institution: | (1) Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH England, UK |
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Abstract: | In the error analysis of the process of interpolation by translates of a single basis function, certain spaces of functions
arise naturally. These spaces are defined with respect to a seminorm which is given in terms of the Fourier transform of the
function. We call this an indirect seminorm. In certain well‐understood cases, the seminorm can be rewritten trivially in
terms of the function, rather than its Fourier transform. We call this a direct seminorm. The direct form allows better error
estimates to be obtained. In this paper, we shown how to rewrite most of the commonly arising indirect form seminorms in direct
form, and begin a little of the analysis required to obtain the improved error estimates.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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