On d-dimensional d-Semimetrics and Simplex-Type Inequalities for High-Dimensional Sine Functions

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dc.creatorLerman, Gilad
dc.creatorWhitehouse, Jonathan Tyler
dc.date2008-05-09
dc.date2009-01-29
dc.date.accessioned2026-07-07T12:35:19Z
dc.date.available2026-07-07T12:35:19Z
dc.descriptionWe show that high-dimensional analogues of the sine function (more precisely, the d-dimensional polar sine and the d-th root of the d-dimensional hypersine) satisfy a simplex-type inequality in a real pre-Hilbert space H. Adopting the language of Deza and Rosenberg, we say that these d-dimensional sine functions are d-semimetrics. We also establish geometric identities for both the d-dimensional polar sine and the d-dimensional hypersine. We then show that when d=1 the underlying functional equation of the corresponding identity characterizes a generalized sine function. Finally, we show that the d-dimensional polar sine satisfies a relaxed simplex inequality of two controlling terms "with high probability".
dc.description22 pages and 2 figures, updated to reflect publication in JAT and the DOI
dc.identifierhttps://arxiv.org/abs/0805.1430
dc.identifierhttp://arxiv.org/abs/0805.1430
dc.identifierJournal of Approximation Theory, 156 (1): 52-81, January 2009
dc.identifierdoi:10.1016/j.jat.2008.03.005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217732
dc.subjectClassical Analysis and ODEs
dc.subjectMetric Geometry
dc.subject46C05, 52C99, 39B05, 60D05, 42B99
dc.titleOn d-dimensional d-Semimetrics and Simplex-Type Inequalities for High-Dimensional Sine Functions
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