Enhanced negative type for finite metric trees
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| 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] |
| Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 31494478 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Enhanced negative type for finite metric trees – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Doust%2C+Ian%22">Doust, Ian</searchLink><relatesTo>1</relatesTo><i> i.doust@unsw.edu.au</i><br /><searchLink fieldCode="AR" term="%22Weston%2C+Anthony%22">Weston, Anthony</searchLink><relatesTo>2</relatesTo><i> westona@canisius.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. May2008, Vol. 254 Issue 9, p2336-2364. 29p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jfa.2008.01.013 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: 2336 Subjects: – SubjectFull: Metric spaces Type: general – SubjectFull: Set theory Type: general – SubjectFull: Graph theory Type: general Titles: – TitleFull: Enhanced negative type for finite metric trees Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Doust, Ian – PersonEntity: Name: NameFull: Weston, Anthony IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2008 Type: published Y: 2008 Identifiers: – Type: issn-print Value: 00221236 Numbering: – Type: volume Value: 254 – Type: issue Value: 9 Titles: – TitleFull: Journal of Functional Analysis Type: main |
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