Abstract
Let S ⊂ \(\mathbb{R}\) 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, sl, s2,…} ∪ {σ}, where (sk){skk=0/∞} is a monotone sequence with σ = limk→∞sk, we give a sufficient and necessary condition for the existence of a so-called Lagrange basis. Furthermore, we show that little q-Jacobi polynomials which fulfill a certain boundedness property constitute a basis in case of Sq, = {1,q, q2,…} ∪ {0}, 0<q<1.
Partially supported by KBN (Poland) under grant 2 P03A 028 25.
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Obermaier, J., Szwarc, R. (2005). Polynomial Bases for Continuous Function Spaces. In: Mache, D.H., Szabados, J., de Bruin, M.G. (eds) Trends and Applications in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 151. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7356-3_14
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DOI: https://doi.org/10.1007/3-7643-7356-3_14
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