30 citations · 416 across the 73 of their papers we have counts for
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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…
The -norm of circulant matrices
Ludovick Bouthat, Apoorva Khare, Javad Mashreghi +1
In this note we study the induced -norm of circulant matrices , acting as operators on the Euclidean space . For circulant matrices whose entries ar…
Multiply positive functions, critical exponent phenomena, and the Jain-Karlin-Schoenberg kernel
Apoorva Khare
We prove the converse to a result of Karlin [Trans. AMS 1964], and also strengthen his result and two results of Schoenberg [Ann. of Math. 1955]. One of the latter results concerns…
Totally positive kernels, Polya frequency functions, and their transforms
Alexander Belton, Dominique Guillot, Apoorva Khare +1
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post…
Total-positivity preservers
Alexander Belton, Dominique Guillot, Apoorva Khare +1
We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an exte…
Preserving positivity for matrices with sparsity constraints
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
Functions preserving Loewner positivity when applied entrywise to positive semidefinite matrices have been widely studied in the literature. Following the work of Schoenberg [Duke…