Abstract
LetP(N,m;r 1,...,r n ) be the class of 1-periodic perfect splines of degreem with 2N knots, which haven distinct zeros in one period with multiplicitiesr 1,...,r n , respectively. We show that there exists a unique extremal elementP *∈P(N,m;r 1,...,r n ) of minimal uniform norm which equioscillates. This problem is related to the optimal recovery of smooth periodic functions on the basis of the Hermitian data.
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