Let f(x) be a function of bounded variation on [-1,1] and S n(f;x) the nth partial sum of the expansion of f(x) in a Chebyshev series of the second kind. In this note we give the estimate for the rate of convergence of the sequence Sn(f;x) to f(x) in terms of the modulus of continuity of the total variation of f(x).
|Number of pages||7|
|Journal||Missouri Journal of Mathematical Sciences|
|Publication status||Published - 2002|
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