Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials

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 Erdös-Turán-type inequalities, approximations to other periodic functions and bounds for certain Hermitian forms.

14 pages. Accepted for publication in the J. Approx. Theory. V2 has additional references and some typos corrected

References in corpus (1)

• Some extremal functions in Fourier analysis, II

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