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, $p_0 2$, such that this family is a Schauder basis of $L_s(0,1)$ for all $s>1$ and $p\in[p_0,p_1]$.
|Number of pages||22|
|Journal||Journal of Mathematical Analysis and Applications|
|Early online date||16 Jun 2016|
|Publication status||Published - 1 Dec 2016|
- Primary: 42A16, Secondary: 42A65