Skip to main content

Distance geometry in quasihypermetric spaces. III

Journal Article


Abstract


  • Let (X, d) be a compact metric space and let M(X) denote the space of all finite signed Borel measures on X. Define I : M(X) → 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 M(X) of total mass 1. This paper, with two earlier papers [Peter Nickolas and Reinhard Wolf, Distance geometry in quasihypermetric spaces. I and II ], 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 M(X) when equipped with a natural semi-inner product. Specifically, this paper explores links between the properties of M(X ) and metric embeddings of X, and the properties of M(X) when X is a finite metric space.

Publication Date


  • 2011

Citation


  • Nickolas, P. & Wolf, R. (2011). Distance geometry in quasihypermetric spaces. III. Mathematische Nachrichten, 284 (5-6), 747-760.

Scopus Eid


  • 2-s2.0-84911497379

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3567

Has Global Citation Frequency


Number Of Pages


  • 13

Start Page


  • 747

End Page


  • 760

Volume


  • 284

Issue


  • 5-6

Place Of Publication


  • Germany

Abstract


  • Let (X, d) be a compact metric space and let M(X) denote the space of all finite signed Borel measures on X. Define I : M(X) → 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 M(X) of total mass 1. This paper, with two earlier papers [Peter Nickolas and Reinhard Wolf, Distance geometry in quasihypermetric spaces. I and II ], 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 M(X) when equipped with a natural semi-inner product. Specifically, this paper explores links between the properties of M(X ) and metric embeddings of X, and the properties of M(X) when X is a finite metric space.

Publication Date


  • 2011

Citation


  • Nickolas, P. & Wolf, R. (2011). Distance geometry in quasihypermetric spaces. III. Mathematische Nachrichten, 284 (5-6), 747-760.

Scopus Eid


  • 2-s2.0-84911497379

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/3567

Has Global Citation Frequency


Number Of Pages


  • 13

Start Page


  • 747

End Page


  • 760

Volume


  • 284

Issue


  • 5-6

Place Of Publication


  • Germany