Computational Methods and Function Theory 1 (2001), No. 1, 193--204
Copyright Heldermann Verlag 2001
Brigitte Forster
forsterb@ma.tum.de, Zentrum Mathematik, Technische Universität München, Arcisstr. 21, 80290 München, Germany.
Yu.~I.~Mel'nik showed in \cite{melnik84} that under certain conditions the Leont'ev coefficients $\kappa_{f}(\lambda)$ in the Dirichlet series $$ f \sim \sum_{\lambda\in\Lambda} \kappa_{f}(\lambda) \frac{e^{\lambda\cdot}}{L^{\prime}(\lambda)} $$ of a function $f\in AC(\overline{D})$ are the Fourier coefficients of some continuous $2\pi$-periodic function. He showed the relationship between the first moduli of smoothness of these two functions. In this article we will expand his results to moduli of arbitrary order.
Keywords: Dirichlet series, Fourier coefficients, Leont'ev coefficients.
MSC 2000: 30B50, 42A16.
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