Isometric embeddings of snowflakes into finite-dimensional Banach spaces
Le Donne, E., Rajala, T., & Walsberg, E. (2018). Isometric embeddings of snowflakes into finite-dimensional Banach spaces. Proceedings of the American Mathematical Society, 146(2), 685-693. https://doi.org/10.1090/proc/13778
Julkaistu sarjassa
Proceedings of the American Mathematical SocietyPäivämäärä
2018Tekijänoikeudet
© 2017 American Mathematical Society
We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a
metric space X isometrically embeds into some finite-dimensional normed space if
and only if X is finite. In the case of power functions we give a uniform bound on
the cardinality of X depending only on the power exponent and the dimension of
the vector space.
Julkaisija
American Mathematical SocietyISSN Hae Julkaisufoorumista
0002-9939Asiasanat
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https://converis.jyu.fi/converis/portal/detail/Publication/27796618
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Akatemiatutkija, SA
Lisätietoja rahoituksesta
The first and second authors acknowledge the support of the Academy of Finland, projects no. 288501 and 274372 The third author acknowledges the support of the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 291111/ MODAGLisenssi
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