Regularity properties of the element of closest approximation
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- by Harold S. Shapiro PDF
- Trans. Amer. Math. Soc. 181 (1973), 127-142 Request permission
Abstract:
Given an element $f \epsilon {L^p}(T),1 < p < \infty$, and a closed translation invariant subspace $S$ of ${L^p}(T)$, we investigate the regularity (smoothness) properties of the element of $S$ which is closest to $f$. The regularity of this element is in general less than that of $f$. The problem reveals a surprising connection with a hitherto unstudied class of extremal Fourier multipliers.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 181 (1973), 127-142
- MSC: Primary 42A08; Secondary 41A50
- DOI: https://doi.org/10.1090/S0002-9947-1973-0320606-6
- MathSciNet review: 0320606