30 citations · 416 across the 73 of their papers we have counts for
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Loewner positive entrywise functions, and classification of measurable solutions of Cauchy's functional equations
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
Entrywise functions preserving Loewner positivity have been studied by many authors, most notably Schoenberg and Rudin. Following their work, it is known that functions preserving…
Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
Entrywise powers of symmetric matrices preserving positivity, monotonicity or convexity with respect to the Loewner ordering arise in various applications, and have received much a…
Weights of simple highest weight modules over a complex semisimple Lie algebra
Apoorva Khare
In this short note we announce three formulas for the set of weights of various classes of highest weight modules $\V$ with highest weight λ, over a complex semisimple Lie algebra…
The critical exponent conjecture for powers of doubly nonnegative matrices
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
Doubly non-negative matrices arise naturally in many setting including Markov random fields (positively banded graphical models) and in the convergence analysis of Markov chains. I…
Faces and maximizer subsets of highest weight modules
Apoorva Khare
In this paper we study general highest weight modules over a complex finite-dimensional semisimple Lie algebra . We present three formulas for the set…