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Inverse Approximation Theorems for Dirichlet Series in AC(D‾)

B. Forster

East Journal on Approximations, vol. 9, no. 3, pp. 305-322, September 2003.



We consider functions ƒ ∈ AC(D‾) on a convex polygon DC and their Dirichlet expansion

ƒ(z) ∼ ∑(λ∈Λ) κƒ(λ) eλ zL′(λ).

The order of convergence is related to the regularity of ƒ with respect to Tamrazov's moduli of smoothness. We give an extension of the inverse approximation theorem by Mel′nik in [1] with respect to moduli of arbitrary order kN.

References

  1. Y.I. Mel′nik, "Approximation of Functions Regular in Convex Polygons by Exponential Polynomials," Ukrainian Mathematical Journal, vol. 40, no. 4, pp. 382-387, April 1988.


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AUTHOR="Forster, B.",
TITLE="Inverse Approximation Theorems for Dirichlet Series in
        {$AC(\bar{D})$}",
JOURNAL="East Journal on Approximations",
YEAR="2003",
volume="9",
number="3",
pages="305--322",
month="September",
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