Metric projection onto finite-dimensional subspaces of C and L |
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Authors: | V I Berdyshev |
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Institution: | 1. Institute of Mathematics and Mechanics of the General Science Center, Academy of Sciences of the USSR, USSR
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Abstract: | In the space C(Q) of real functions that are continuous on the compact set Q, a finite-dimensional subspace P will have a uniformly continuous metric projection if and only if Q is a finite sum of compact sets Qi, and either P is on each Qi a one-dimensional Chebyshev space, or x(t)≡0 for any x belonging to P. The metric projection onto any finite-dimensional subspace of the space La, b] of real integrable functions is not uniformly continuous. |
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