Apoorva Khare

collaborators

6 papers

math.RA2025

Cholesky decomposition for symmetric matrices, Riemannian geometry, and random matrices

Apoorva Khare, Prateek Kumar Vishwakarma

For each $n \geq 1$ and sign pattern $ε \in {\pm 1}^{n}$ , we introduce a cone of real symmetric matrices $L P M_{n} (ε)$ : those with leading principal $k \times k$ minors of signs $ε_k…

math.NT2025

Maps preserving the sum-to-difference ratio in characteristic $p$

Sunil Chebolu, Apoorva Khare, Anindya Sen

Given a field $F$ , we introduce a novel group $S D (F)$ of its self-maps: the solutions $f : F ↠ F$ to the functional equati…

math.NT2025

Maps preserving the sum-to-difference ratio

Sunil Chebolu, Apoorva Khare, Anindya Sen

For a field $F$ , what are all functions $f : F \to F$ that satisfy the functional equation $f \left( (x+y)/(x-y) \right) = (f(x) + f(y))/(f(…

math.RT2025

Log-concavity of characters of parabolic Verma modules, and of restricted Kostant partition functions

Apoorva Khare, Jacob P. Matherne, Avery St. Dizier

In 2022, Huh-Matherne-Mészáros-St. Dizier showed that normalized Schur polynomials are Lorentzian, thereby yielding their continuous (resp. discrete) log-concavity on the positive…

math.FA2025

Numerical radius and $ℓ_{p}$ operator norm of Kronecker products and Schur powers: inequalities and equalities

Pintu Bhunia, Sujit Sakharam Damase, Apoorva Khare

Suppose $A = [a_{ij}] \in M_{n} (C)$ is a complex $n \times n$ matrix and $B \in B (H)$ is a bounded linear operator on a complex Hilbert space $\mat…

math.FA2024

Multivariate transforms of total positivity

Sujit Sakharam Damase, Apoorva Khare

Belton-Guillot-Khare-Putinar [J. d'Analyse Math. 2023] classified the post-composition operators that preserve TP/TN kernels of each specified order. We explain how to extend this…