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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.


  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.

AUTHOR="Forster, B.",
TITLE="Inverse Approximation Theorems for Dirichlet Series in
JOURNAL="East Journal on Approximations",

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