Polynomial bases for continuous function spaces

Abstract

Let S ⊂ R denote a compact set with infinite cardinality and C(S) the set of real continuous functions on S. We investigate the problem of polynomial and orthogonal polynomial bases of C(S). In case of S = {s0, s1, s2, . . .} ∪ {σ}, where (sk)k=0 is a monotone sequence with σ = limk→∞ sk, we give a sufficient and necessary condition for the existence of a… (More)

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