ar X iv : 0 70 8 . 28 83 v 2 [ m at h . C A ] 2 1 A ug 2 00 7 POSITIVE BASES IN SPACES OF POLYNOMIALS
نویسندگان
چکیده
For a nonempty compact set Ω ⊆ R we determine the maximal possible dimension of a subspace X ⊆ Pm(Ω) of polynomial functions over Ω with degree at most m which possesses a positive basis. The exact value of this maximum depends on topological features of Ω, and we will see that in many of the cases m can be achieved. Whereas only for low m or finite sets Ω is it possible that we have a subspace X with positive basis and with dim X = m + 1. Hence there is no Ω for which a positive basis exists in Pm for all m ∈ N.
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