Bibliographic Details
| Title: |
Enhanced negative type for finite metric trees |
| Authors: |
Doust, Ian1 i.doust@unsw.edu.au, Weston, Anthony2 westona@canisius.edu |
| Source: |
Journal of Functional Analysis. May2008, Vol. 254 Issue 9, p2336-2364. 29p. |
| Subjects: |
Metric spaces, Set theory, Graph theory |
| Abstract: |
Abstract: A finite metric tree is a finite connected graph that has no cycles, endowed with an edge weighted path metric. Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities (1) that encode the best possible quantification of the strictness of the non-trivial 1-negative type inequalities for finite metric trees. These inequalities are sufficiently strong to imply that any given finite metric tree must have strict p-negative type for all p in an open interval , where may be chosen so as to depend only upon the unordered distribution of edge weights that determine the path metric d on T. In particular, if the edges of the tree are not weighted, then it follows that ζ depends only upon the number of vertices in the tree. We also give an example of an infinite metric tree that has strict 1-negative type but does not have p-negative type for any . This shows that the maximal p-negative type of a metric space can be strict. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
