Minimal Lp projections by Fourier, Taylor, and Laurent series |
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| Authors: | B. L. Chalmers J. C. Mason |
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| Affiliation: | Department of Mathematics, University of California, Riverside, California, 92521, U.S.A.;Mathematics and Ballistics Branch, Royal Military College of Science, Shrivenham, Swindon, Wiltshire, England |
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| Abstract: | In appropriate function space settings, it is proved that the Fourier, Taylor, and Laurent series projections are minimal in all Lp norms (1 p ∞). This result unifies and extends known results for the Fourier, Taylor, and Laurent projections in L∞ and for the Fourier projection in L1. The proof is based on a generalisation of a kernel summation formula due to Berman. |
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