71 citations · 300 across the 27 of their papers we have counts for
30 papers
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…
Positivity preservers over finite fields
Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma +1
We resolve an algebraic version of Schoenberg's celebrated theorem [Duke Math.J., 1942] characterizing entrywise matrix transforms that preserve positive definiteness. Compared to…
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…
Preservers of totally positive kernels and Polya frequency functions
Alexander Belton, Dominique Guillot, Apoorva Khare +1
Fractional powers and polynomial maps preserving structured totally positive matrices, one-sided Polya frequency functions, or totally positive kernels are treated from a unifying…
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…