22 citations · 61 across the 6 of their papers we have counts for
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math.MG2008★ 17 cited
High-Dimensional Menger-Type Curvatures-Part II: d-Separation and a Menagerie of Curvatures
Gilad Lerman, J. Tyler Whitehouse
This is the second of two papers wherein we estimate multiscale least squares approximations of certain measures by Menger-type curvatures. More specifically, we study an arbitrary…
math.CA2008★ 22 cited
On d-dimensional d-Semimetrics and Simplex-Type Inequalities for High-Dimensional Sine Functions
Gilad Lerman, Jonathan Tyler Whitehouse
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…
math.CA2008★ 15 cited
High-Dimensional Menger-Type Curvatures - Part I: Geometric Multipoles and Multiscale Inequalities
G. Lerman, J. T. Whitehouse
We define a discrete Menger-type curvature of d+2 points in a real separable Hilbert space H by an appropriate scaling of the squared volume of the corresponding (d+1)-simplex. We…