On local linear functionals which vanish at all B-splines but one
نویسنده
چکیده
The first such linear functional seems to have been constructed in [1], for the purpose of demonstrating the linear independence over an interval of all B-splines which do not vanish identically on that interval. Since then, such linear functionals have been constructed in various ways and for a variety of jobs [2] – [7], [11], [13], [16], some of which are listed in Section 2. In particular, it was shown in [6] that there exists a smallest number Dk so that, for all t and all i with ti < ti+k, an hi ∈ IL∞ can be found with supphi ⊆ [ti, ti+k], ‖hi‖∞ ≤ Dk/(ti+k − ti), and ∫ hiNj = δij , all j. After a discussion in Section 3 as to how to construct linear functionals λi satisfying (1.2), it is shown in Section 4 that (π/2)/2 ≤ Dk ≤ 2k 9. Also, numerical evidence is presented to indicate that probably
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