Polynomial approximation of piecewise analytic functions on quasi-smooth arcs

Liudmyla Kryvonos

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arXiv · 2102.01848

Polynomial approximation of piecewise analytic functions on quasi-smooth arcs

Liudmyla Kryvonos

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Abstract

For a function $f$ that is piecewise analytic on a quasi-smooth arc $\mathcal{L}$ and any $0<\sigma<1$ we construct a sequence of "near-best" polynomials that converge at a rate $e^{-n^{\sigma}}$ at each point of analyticity of $f$ and are close to the best polynomial approximants on the whole $\mathcal{L}$. Also we give examples of quasi-smooth arcs for which convergence of "near-best" approximants at points of analiticity of $f$ is geometric, i.e. has a rate $e^{-cn}$ with some $c>0$.

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BibTeX RIS

Liudmyla Kryvonos. 2021-02-03. Polynomial approximation of piecewise analytic functions on quasi-smooth arcs. https://arxiv.org/abs/2102.01848

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