An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-R\'enyi Entropy Power Inequality for Integer Valued Random Variables

Peng Xu; Mokshay Madiman; James Melbourne

An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-R\'enyi Entropy Power Inequality for Integer Valued Random Variables

Functional Analysis 2018-08-24 v1 Information Theory math.IT Probability

Authors: Peng Xu , Mokshay Madiman , James Melbourne

Abstract

In this paper, we proved an exact asymptotically sharp upper bound of the $L^p$ Lebesgue Constant (i.e. the $L^p$ norm of Dirichlet kernel) for $p\ge 2$ . As an application, we also verified the implication of a new $\infty$ -R\'enyi entropy power inequality for integer valued random variables.

Keywords

L^p Lebesgue constant Dirichlet kernel asymptotically sharp upper bound Rényi entropy power inequality integer valued random variables

Cite

@article{arxiv.1808.07732,
  title  = {An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-R\'enyi Entropy Power Inequality for Integer Valued Random Variables},
  author = {Peng Xu and Mokshay Madiman and James Melbourne},
  journal= {arXiv preprint arXiv:1808.07732},
  year   = {2018}
}

Comments

13 pages, 2 figures

An Exact Upper Bound on the $L^p$ Lebesgue Constant and The $\infty$-R\'enyi Entropy Power Inequality for Integer Valued Random Variables

Abstract

Keywords

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