Abstract
We estimate the rate of covergence to functions in the spacesL p [0,1] and C[0,1] by polynomial of the form ∑ λ α λ x λ, where the λ′s are positive real numbers and 0.
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References
J. Bak and D. J. Newman,Müntz-Jackson theorems in L p and C, Amer. J. Math.154 (1972), 437–457.
J. Bak and D. J. Newman,Müntz-Jackson theorems in L p,p<2, J. Approximation Theory, to appear.
T. Ganelius and S. Westlund,Degree of approximation in Müntz's theorem, Proc. Int. Conf. on Math. Anal., Jyväskylä, Finland, 1970.
D. Jackson,The Theory of Appromixation, A. M. S. Colloquium Pubs., Vol. XI, New York, 1930.
D. Leviatan,On the Jackson-Müntz theorem, J. Approximation Theory, to appear.
D. J. Newman,A general Müntz-Jackson theorem, Amer. J. Math., to appear.
D. J. Newman,Müntz-Jackson Theorem in L 2, J. Approximation Theory, to appear.
A. F. Timan,Theory of Approximation of Functions of a Real Variable, Pergamon Press, New York, 1963.
M. Von Golitschek,Erweiterung der Approximationssatze von Jackson im Sinne von Ch. Müntz II, J. Approximation Theory3 (1970), 72–85.
A. Zygmund,Trigonometrical Series, Monografje Mathematyczne, Tom V, Warszawa-Lwow, 1935.
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Bak, J., Leviatan, D., Newman, D.J. et al. Generalized polynomial approximation. Israel J. Math. 15, 337–349 (1973). https://doi.org/10.1007/BF02757072
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DOI: https://doi.org/10.1007/BF02757072