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 D ⊂ C and their Dirichlet expansion
ƒ(z) ∼ ∑(λ∈Λ) κƒ(λ) eλ z ⁄ L′(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 k ∈ N.
References
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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.
@ARTICLE(http://bigwww.epfl.ch/publications/forster0301.html,
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",
note="")
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