Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T07:22:40.807Z Has data issue: false hasContentIssue false

Packing of spheres in lp

Published online by Cambridge University Press:  18 May 2009

E. Spence
Affiliation:
University of Glasgow, Glasgow, W.2.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Banach space lp(p≥1) is the space of all infinite sequences x = (x1, x2, x3, …) of real or complex numbers such that is convergent, with the norm defined by

The unit sphere S of lp is the set of all points x ∈ lp with ∥x∥ ≤ 1 and the sphere of radius a ≥ 0 centred at y ∈ lp is denoted by Sa(y), so that

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Burlak, Jane A. C., Rankin, R. A. and Robertson, A. P., The packing of spheres in the space lp, Proc. Glasgow Math. Assoc. 4 (1958), 2225.CrossRefGoogle Scholar
2.Rankin, R. A., On sums of powers of linear forms I, Ann. of Math. 50 (1949), 691698.CrossRefGoogle Scholar
3.Rankin, R. A., On sums of powers of linear forms II, Ann. of Math. 50 (1949), 699704.CrossRefGoogle Scholar