Abstract
When the output from a physical process is entirely a smoothed or blurred version of the input, we should not expect to be able to recover the input from the output, since unsmoothing presumably is not a stable, continuous process. Irregularities and fine details of the input are lost beyond recovery in the smoothing operation. This means that integral equations of the first kind usually do not have solutions. Those that we considered in the preceding chapter actually involve differential-integral operators that do not have a pronounced smoothing effect.
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© 1991 Springer Science+Business Media New York
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Pipkin, A.C. (1991). Smoothing and Unsmoothing. In: A Course on Integral Equations. Texts in Applied Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4446-2_7
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DOI: https://doi.org/10.1007/978-1-4612-4446-2_7
Publisher Name: Springer, New York, NY
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