Local convergence of Fourier series with respect to periodized wavelets
Journal of Approximation Theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A uniform asymptotic expansion for Jacobi polynomials via uniform treatment of Darboux's method
Journal of Approximation Theory
Polynomial operators and local smoothness classes on the unit interval
Journal of Approximation Theory
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In our paper we construct a polynomial Schauder basis (p"@a","@b","n)"n"@?"N"""0 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] and as the main difficulty of the whole proof we show the uniform boundedness of its Lebesgue constants supx@?[-1,1],n@?N"0@?@?j=0np"@a","@b","j(x)p"@a","@b","j@?"L"@w"""@a""","""@b"1"["-"1","1"]