Name
Title | ||
|---|---|---|
On d-dimensional d-semimetrics and simplex-type inequalities for high-dimensional sine functions |
Abstract | ||
|---|---|---|
We 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''. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jat.2008.03.005 | Journal of Approximation Theory |
Keywords | DocType | Volume |
geometric inequalities,d-dimensional sine function,d-th root,polar sine,ahlfors regular measure.,pre-hilbert space,d-semimetrics,concentra- tion inequalities,. high-dimensional geometry,d-dimensional polar sine,corresponding identity,simplex-type inequality,generalized sine function,high-dimensional sine function,sine function,simplex inequality,controlling term,hypersine,d-dimensional hypersine,d-dimensional d-semimetrics,functional equations in several variables,trigonometric identities,satisfiability,hilbert space,functional equation | Journal | 156 |
Issue | ISSN | Citations |
1 | Journal of Approximation Theory, 156 (1): 52-81, January 2009 | 10 |
PageRank | References | Authors |
0.71 | 6 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gilad Lerman | 1 | 481 | 26.33 |
| J. Tyler Whitehouse | 2 | 13 | 1.09 |