Generalised cosine functions, basis and regularity properties

Lyonell Boulton; Houry Melkonian

doi:10.1016/j.jmaa.2016.06.024

Generalised cosine functions, basis and regularity properties

Lyonell Boulton
, Houry Melkonian

Research output: Contribution to journal › Article › peer-review

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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, $p_0 2$, such that this family is a Schauder basis of $L_s(0,1)$ for all $s>1$ and $p\in[p_0,p_1]$.

Original language	English
Pages (from-to)	25–46
Number of pages	22
Journal	Journal of Mathematical Analysis and Applications
Volume	444
Issue number	1
Early online date	16 Jun 2016
DOIs	https://doi.org/10.1016/j.jmaa.2016.06.024
Publication status	Published - 1 Dec 2016

Keywords

math.CA
Primary: 42A16, Secondary: 42A65

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10.1016/j.jmaa.2016.06.024

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title = "Generalised cosine functions, basis and regularity properties",

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\$, such that this family is a Schauder basis of \$L\_s(0,1)\$ for all \$s>1\$ and \$p\textbackslash{}in[p\_0,p\_1]\$.",

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AU - Melkonian, Houry

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N2 - 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 $p\in[p_0,p_1]$.

AB - 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 $p\in[p_0,p_1]$.

KW - math.CA

KW - Primary: 42A16, Secondary: 42A65

U2 - 10.1016/j.jmaa.2016.06.024

DO - 10.1016/j.jmaa.2016.06.024

M3 - Article

SN - 0022-247X

VL - 444

SP - 25

EP - 46

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Generalised cosine functions, basis and regularity properties

Abstract

Keywords

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