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On the minimal property of the Fourier projection

1969
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Bulletin of the American Mathematical Society
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Let C be the space of real 27r-periodic continuous functions normed with the supremum norm. Let P n denote the subspace of trigonometric polynomials of degree ^n. It is known [l] that the Fourier projection F of C onto P» is minimal; i.e., if A is a projection of C onto P n then \\F\\ Û\\A\\. We prove that F is the only minimal projection of C onto P n . The proof is constructed by verifying the assertions listed below. Details will appear elsewhere. ASSERTION. If there exists a minimal

doi:10.1090/s0002-9904-1969-12141-5
fatcat:vk5wmck7tbgwjahoj3x5sgwjpu