A continuous function space with a Faber basis Original Research Article

Let S⊂R be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (Pn)n=0∞ with deg Pn=n such that every f∈C(S) has a unique representation f=∑i=0∞ αiPi and call such a basis Faber basis. In the special case of S=Sq={qk;k∈N0}∪{0}, 0