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Approximated Leont′ev Coefficients

B. Forster

Journal of Computational Analysis and Applications, vol. 7, no. 2, pp. 123-134, April 2006.

We consider Dirichlet series on convex polygons and their rate of approximation in AC(D‾). We show that the substitution of the respective Leont′ev coefficients by appropriate interpolating sums preserves the order of approximation up to a factor ln n. The estimates are given for moduli of smoothness of arbitrary order. This extends a result of Yu. I. Mel′nik in [1].


  1. Y.I. Mel′nik, "On Approximation of Functions Regular in Convex Polygons by Exponential Polynomials of Special Form," Ukrainian Mathematical Journal, vol. 44, no. 3, pp. 368-370, March 1992.

AUTHOR="Forster, B.",
TITLE="Approximated {L}eont'ev Coefficients",
JOURNAL="Journal of Computational Analysis and Applications",

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