Apoorva Khare

activity

20182026

most citedHomogeneous length functions on groups

9 citations · 11 across the 10 of their papers we have counts for

collaborators

11 papers

math.CO2026

A tight bound for affine-linearity, via universal ballot matrices

Apoorva Khare, Ashwin Sah

Based on work with Greenfeld and with Ziegler, Tao showed a concatenation result that if a map $f : F^{2} \to F$ is affine-linear on every line parallel to the coor…

math.CA2025

The entrywise calculus and dimension-free positivity preservers, with an Appendix on sphere packings

Apoorva Khare

We present an overview of a classical theme in analysis and matrix positivity: the question of which functions preserve positive semidefiniteness when applied entrywise. In additio…

math.CO2025

Majorization via positivity of Jack and Macdonald polynomial differences

Hong Chen, Apoorva Khare, Siddhartha Sahi

Majorization inequalities have a long history, going back to Maclaurin and Newton. They were recently studied for several families of symmetric functions, including by Cuttler--Gre…

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★ 1 cited

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…

math.FA2023★ 1 cited

A remark on characterizing inner product spaces via strong three-point homogeneity

Sujit Sakharam Damase, Apoorva Khare

We show that a normed linear space is isometrically isomorphic to an inner product space if and only if it is a strongly $n$ -point homogeneous metric space for any (or every) $n \g…

math.GR2018★ 9 cited

Homogeneous length functions on groups

D. H. J. Polymath

A pseudo-length function defined on an arbitrary group $G = (G, \cdot, e, ()^{- 1})$ is a map $ℓ : G \to [0, + \infty)$ obeying $ℓ (e) = 0$ , the symmetry property $\ell(x^{-1}) = \e…