Distance Geometry in Quasihypermetric Spaces. II
| dc.creator | Nickolas, Peter | |
| dc.creator | Wolf, Reinhard | |
| dc.date | 2008-09-04 | |
| dc.date.accessioned | 2026-07-07T10:00:38Z | |
| dc.date.available | 2026-07-07T10:00:38Z | |
| dc.description | Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by \[ I(μ) = \int_X \int_X d(x,y) dμ(x) dμ(y), \] and set $M(X) = \sup I(μ)$, where $μ$ ranges over the collection of signed measures in $\mathcal{M}(X)$ of total mass 1. This paper, with an earlier and a subsequent paper [Peter Nickolas and Reinhard Wolf, Distance geometry in quasihypermetric spaces. I and III], investigates the geometric constant $M(X)$ and its relationship to the metric properties of $X$ and the functional-analytic properties of a certain subspace of $\mathcal{M}(X)$ when equipped with a natural semi-inner product. Using the work of the earlier paper, this paper explores measures which attain the supremum defining $M(X)$, sequences of measures which approximate the supremum when the supremum is not attained and conditions implying or equivalent to the finiteness of $M(X)$. | |
| dc.description | 15 pages. References [8] and [9] are arXiv:0809.0740v1 [math.MG] and arXiv:0809.0746v1 [math.MG] | |
| dc.identifier | https://arxiv.org/abs/0809.0744 | |
| dc.identifier | http://arxiv.org/abs/0809.0744 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168375 | |
| dc.subject | Metric Geometry | |
| dc.subject | 51K05 (Primary) 54E45, 31C45 (Secondary) | |
| dc.title | Distance Geometry in Quasihypermetric Spaces. II | |
| dc.type | text |