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arXiv · 0809.4049

Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials

Emanuel Carneiro
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Abstract

We obtain optimal trigonometric polynomials of a given degree $N$ that majorize, minorize and approximate in $L^1(\mathbb{R}/\mathbb{Z})$ the Bernoulli periodic functions. These are the periodic analogues of two works of F. Littmann that generalize a paper of J. Vaaler. As applications we provide the corresponding Erd\"{o}s-Tur\'{a}n-type inequalities, approximations to other periodic functions and bounds for certain Hermitian forms.

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BibTeXRIS

Emanuel Carneiro. 2008-09-23. Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials. https://doi.org/10.1016/j.jat.2008.03.007

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