Inequalities and sphere-packing in \(\ell _ p\)
type: Item
instance of: scholarly article
title: Inequalities and sphere-packing in \(\ell _ p\)
zbMATH Open document ID: 0642.46021
DOI: 10.1007/BF02785681
published in: Israel Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Consider the classical sequence spaces \(\ell^ r\), \(1\leq p<\infty\); least upper bounds for the set of real numbers \(r_ p\) such that infinitely many balls of radius \(r_ p\) can be packed in the unit ball of \(\ell^ p\) are known. For \(\rho >r_ p\) it is interesting to know the maximum (finite) number of balls of radius \(\rho\) which can be packed in \(\ell^ p:\) some estimates go back to \textit{J. A. C. Burlak}, \textit{R. A. Rankin} and \textit{P. A. Robertson}, Proc. Glasgow Math. Assoc. 4, 22-25 (1958; Zbl 0087.108). By using nice inequalities, sharp estimates concerning the above numbers are given in the present paper, both for the case \(1\leq p\leq 2\) and for \(2\leq p<\infty\). Also, by combining Theorem 10 here with some results by \textit{D. Amir} [Pac. J. Math. 118, 1-15 (1985; Zbl 0529.46011)] the value of the Jung constant in \(\ell^ p\) (p\(\neq 2)\) is obtained.
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 4046390
zbMATH Keywords: sharp estimates
zbMATH Keywords: Jung constant
author: Keith Ball
reviewed by: Pier Luigi Papini
MaRDI profile type: Publication
cites work: Isometric embedding in \(\ell_ p\)-spaces
cites work: Q5514858
cites work: The Packing of Spheres in the Space lp
cites work: The unit ball of every infinite-dimensional normed linear space contains a (1+ɛ)-separated sequence
cites work: On sums of powers of linear forms. I
cites work: On sums of powers of linear forms. II
cites work: Q4087773
full work available at URL: https://doi.org/10.1007/bf02785681
OpenAlex ID: W1976765111
description: scientific article; zbMATH DE number 4046390