Polynomial Schauder basis of optimal degree with Jacobi orthogonality

In our paper we construct a polynomial Schauder basis (pα,β,n)n∈N0(pα,β,n)n∈N0 of optimal degree with Jacobi orthogonality. A candidate for such a basis is given by the use of some wavelet theoretical methods, which were already successful in the case of Tchebysheff and Legendre orthogonality. To prove that this sequence is in fact a Schauder basis for C[−1,1]C[−1,1] and as the main difficulty of the whole proof we show the uniform boundedness of its Lebesgue constants supx∈[−1,1],n∈N0‖∑j=0npα,β,j(x)pα,β,j‖Lωα,β1[−1,1]<∞.