Abstract
Let Sn[f](x) be the n-th partial sum of the orthonormal polynomial series expansion for f corresponding to a Freud weight W(x)=e−Q(x). We give a sufficient condition for the inequality
to hold. This sufficient condition is much easier to apply than that of Jha and Lubinsky [2].
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References
Askey, R. and Wainger, S., Mean Convergence of Expansions in Laguerre and Hermite Series, Amer. J. Math., 87(1965), 695–708.
Jha, S. W. and Lubinsky, D. S., Necessary and Sufficient Conditions for Mean Convergence of Orthogonal Expansions for Freud Weights, Constr. Approx., 11(1995), 331–363.
Lubinsky, D. S., Weierstrass Theorem in the Twentieth Century: a Selection, Quaes. Math., 18 (1995), 91–130.
Muckenhoupt, B., Mean Convergence of Hermite and Laguerre Series I, Trans. Amer. Math. Soc., 147(1970), 433–460.
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Lee, D.W. A sufficient condition for mean convergence of orthogonal series for Freud weights. Approx. Theory & its Appl. 16, 55–67 (2000). https://doi.org/10.1007/BF02837631
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DOI: https://doi.org/10.1007/BF02837631