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dc.contributor.author | Arnau-Notari, Andres Roger | es_ES |
dc.contributor.author | Calabuig, J. M. | es_ES |
dc.contributor.author | Sánchez Pérez, Enrique Alfonso | es_ES |
dc.date.accessioned | 2023-06-21T18:01:55Z | |
dc.date.available | 2023-06-21T18:01:55Z | |
dc.date.issued | 2022-10 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/194462 | |
dc.description.abstract | [EN] Here, we prove some general results that allow us to ensure that specific representations (as well as extensions) of certain Lipschitz operators exist, provided we have some additional information about the underlying space, in the context of what we call enriched metric spaces. In this conceptual framework, we introduce some new classes of Lipschitz operators whose definition depends on the notion of metric coordinate system, which are defined by specific dominance inequalities involving summations of distances between certain points in the space. We analyze ¿Pietsch Theorem inspired factorizations" through subspaces of `¿ and L1, which are proved to characterize when a given metric space is Lipschitz isomorphic to a metric subspace of these spaces. As an application, extension results for Lipschitz maps that are obtained by a coordinate-wise adaptation of the McShane¿Whitney formulas, are also given. | es_ES |
dc.description.sponsorship | The first author was supported by a contract of the Programa de Ayudas de Investigacion y Desarrollo (PAID-01-21), Universitat Politecnica de Valencia. The third author was supported by Grant PID2020-112759GB-I00 funded by MCIN/AEI/10.13039/501100011033. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | MDPI AG | es_ES |
dc.relation.ispartof | Mathematics | es_ES |
dc.rights | Reconocimiento (by) | es_ES |
dc.subject | Lipschitz | es_ES |
dc.subject | Operator | es_ES |
dc.subject | Metric space | es_ES |
dc.subject | Extension | es_ES |
dc.subject | Metric coordinates | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | Representation of Lipschitz Maps and Metric Coordinate Systems | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.3390/math10203867 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-112759GB-I00/ES/METAESTRUCTURAS HIPERUNIFORMES/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/UPV-VIN//PAID-01-21//Extensiones de Lipschitz en modelos de Aprendizaje Automático: Aplicaciones al fútbol predictivo basado en datos/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos - Escola Tècnica Superior d'Enginyers de Camins, Canals i Ports | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros Industriales - Escola Tècnica Superior d'Enginyers Industrials | es_ES |
dc.description.bibliographicCitation | Arnau-Notari, AR.; Calabuig, JM.; Sánchez Pérez, EA. (2022). Representation of Lipschitz Maps and Metric Coordinate Systems. Mathematics. 10(20):1-23. https://doi.org/10.3390/math10203867 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.3390/math10203867 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 23 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 10 | es_ES |
dc.description.issue | 20 | es_ES |
dc.identifier.eissn | 2227-7390 | es_ES |
dc.relation.pasarela | S\474914 | es_ES |
dc.contributor.funder | AGENCIA ESTATAL DE INVESTIGACION | es_ES |
dc.contributor.funder | UNIVERSIDAD POLITECNICA DE VALENCIA | es_ES |