30 citations · 416 across the 73 of their papers we have counts for
12 papers · 1 filter
Distance preservers for Lobachevsky space
Alexander Belton, Dominique Guillot, Apoorva Khare +1
We obtain a complete description of the class of entrywise preservers of Lorentz-Gram matrices. This resolves, for the case of constant negative curvature, the classification of en…
Matrix positivity preservers in fixed dimension. II: positive definiteness and strict monotonicity of Schur function ratios
Alexander Belton, Dominique Guillot, Apoorva Khare +1
We continue the study of real polynomials acting entrywise on matrices of fixed dimension to preserve positive semidefiniteness, together with the related analysis of order propert…
Negativity-preserving transforms of tuples of symmetric matrices
Alexander Belton, Dominique Guillot, Apoorva Khare +1
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obta…
Hirschman-Widder densities
Alexander Belton, Dominique Guillot, Apoorva Khare +1
Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations of one-sided exponential functions. The members of this class are probability dens…
Sharp nonzero lower bounds for the Schur product theorem
Apoorva Khare
By a result of Schur [J. Reine Angew. Math. 1911], the entrywise product of two positive semidefinite matrices is again positive. Vybiral [Adv. Math. 2020] improv…
A panorama of positivity
Alexander Belton, Dominique Guillot, Apoorva Khare +1
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (g…