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arXiv · 1511.01114

Generalised cosine functions, basis and regularity properties

Lyonell Boulton·Houry Melkonian
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Abstract

We examine regularity and basis properties of the family of rescaled $p$-cosine functions. We find sharp estimates for their Fourier coefficients. We then determine two thresholds, $p_0<2$ and $p_1>2$, such that this family is a Schauder basis of $L_s(0,1)$ for all $s>1$ and $p\in[p_0,p_1]$.

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Lyonell Boulton, Houry Melkonian. 2015-11-03. Generalised cosine functions, basis and regularity properties. https://arxiv.org/abs/1511.01114

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