Abstract
The uniqueness of monosplines and perfect splines of leastL p-norm is treated in the framework of generalized monosplines and total positivity. The analysis is based on the invariance properties of the degree of a certain mapping and on a new composition result for totally positive kernels. For theL p-case 1<p<∞, uniqueness is shown under the same extra conditions as were previously shown to be needed in theL p-case. The uniqueness in theL ∞-case is obtained without any restrictions.
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Communicated by Allan Pinkus.
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Braess, D., Dyn, N. On the uniqueness of generalized monosplines of least Lp-norm. Constr. Approx 2, 79–99 (1986). https://doi.org/10.1007/BF01893418
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DOI: https://doi.org/10.1007/BF01893418