Mathematics – Functional Analysis
Scientific paper
2007-05-03
Mathematics
Functional Analysis
35 pages, no figures. This is the final version of this paper sans diagrams. Please note the corrected statement of Theorem 4.
Scientific paper
Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities that quantify the extent of the "strictness" of the 1-negative type inequalities for finite metric trees. These inequalities of "enhanced 1-negative type" are sufficiently strong to imply that any given finite metric tree must have strict p-negative type for all values of p in an open interval that contains the number 1. Moreover, these open intervals can be characterized purely in terms of the unordered distribution of edge weights that determine the path metric on the particular tree, and are therefore largely independent of the tree's internal geometry. From these calculations we are able to extract a new non linear technique for improving lower bounds on the maximal p-negative type of certain finite metric spaces. Some pathological examples are also considered in order to stress certain technical points.
Doust Ian
Weston Anthony
No associations
LandOfFree
Enhanced negative type for finite metric trees does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Enhanced negative type for finite metric trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enhanced negative type for finite metric trees will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-496945