Utsav Dewan

activity

20222026

collaborators

18 papers

cs.CL2026

Lost in Translation: Why Lower Bias Scores Don't Mean Fairer Models

Harsh Kumar

Bias audits of multilingual language models usually compare a model's average stereotype score in English with its average in another language and read the difference as a differen…

math.FA2026

Boundary behaviour of eigenfunctions and superharmonic functions on harmonic manifolds of purely exponential volume growth

Utsav Dewan

On $X$ , a non-positively curved harmonic manifold of purely exponential volume growth, of dimension $n \geq 3$ , we study certain quantitative aspects of the boundary behavi…

math.CA2026

Cesàro summability of Hölder functions and Talbot effect on rank one Riemannian symmetric spaces of compact type

Utsav Dewan

On rank one Riemannian symmetric spaces of compact type (of dimension $\geq 2$ ), we first obtain a quantitative characterization of Hölder continuity in terms of Cesàro means. In ad…

math.AP2025

Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type

Utsav Dewan, Sanjoy Pusti

In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type $X = U / K$ , of rank $1$ and $2$ , the Sobolev regularity t…

math.CA2025

Regularity and pointwise convergence for dispersive equations on $H^{2}$

Utsav Dewan

In the prototypical setting of non-Euclidean geometry, the 2-dimensional Real Hyperbolic space $H^{2}$ , we consider the Carleson's problem for the Schrödinger equation and i…

math.AP2025

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces

Utsav Dewan

We study the Carleson's problem on Damek-Ricci spaces $S$ for dispersive equations: \begin{equation*} \begin{cases} i\frac{\partial u}{\partial t} +Ψ(\sqrt{-\mathcal{L}} )u=0\:,\:…

math.FA2025

Iterated convolution inequalities on $R^{d}$ and Riemannian Symmetric Spaces of non-compact type

Utsav Dewan

In a recent work (Int Math Res Not 24:18604-18612, 2021), Carlen-Jauslin-Lieb-Loss studied the convolution inequality $f \geq f * f$ on $R^{d}$ and proved that the real integra…

math.AP2025

Maximal estimates and pointwise convergence for solutions of certain dispersive equations with radial initial data on Damek-Ricci spaces

Utsav Dewan

One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schrödinger equ…

math.FA2024

Pointwise convergence of solutions of the Schrödinger equation along general curves on Damek-Ricci spaces

Utsav Dewan

One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schrödinger equ…

math.FA2024

Mapping properties of the Schrödinger maximal function on Damek--Ricci spaces

Utsav Dewan, Swagato K. Ray

For $f \in S^{2} (S)_{o}$ , the collection of radial $L^{2}$ -Schwartz class functions on Damek--Ricci spaces $S$ , we consider the Schrödinger maximal function…

math.DG2024

Estimates of the Poisson kernel on negatively curved Hadamard manifolds

Kingshook Biswas, Utsav Dewan, Arkajit Pal Choudhury

Let $M$ be an $n$ -dimensional Hadamard manifold of pinched negative curvature $- b^{2} \leq K_{M} \leq - a^{2}$ . The solution of the Dirichlet problem at infinity for $M$ leads to the cons…

math.CA2024

Regularity and pointwise convergence of solutions of the Schrödinger operator with radial initial data on Damek-Ricci spaces

Utsav Dewan

One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schrödinger equ…

math.CA2024

Restricted Mean Value Property with non-tangential boundary behavior on Riemannian manifolds

Utsav Dewan

A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP) for domains in $R^{n}$ . Recently, the author along with…

math.CA2023

Initial singularities of positive solutions of the Heat equation on Stratified Lie groups

Utsav Dewan

Let $(G, \circ)$ be a stratified Lie group. We estimate the Hausdorff dimension (with respect to the Carnot-Carathéodory metric) of the singular sets in $G$ , where…

math.CA2023

Boundary exceptional sets for radial limits of superharmonic functions on non-positively curved Harmonic manifolds of purely exponential volume growth

Utsav Dewan

By classical Fatou type theorems in various setups, it is well-known that positive harmonic functions have non-tangential limit at almost every point on the boundary. In this paper…

math.DG2023

Restricted mean value property on Riemannian manifolds

Kingshook Biswas, Utsav Dewan

A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP). While this has so far been studied mainly for domains in $\ma…

math.FA2023

Spectral projections and resolvent estimates on Damek-Ricci spaces and their applications

Mithun Bhowmik, Utsav Dewan

We prove $L^{p} - L^{p^{'}}$ boundedness of spectral projections and the resolvent of the Laplace-Beltrami operator on Damek-Ricci spaces with the explicit norms in terms of the spe…

math.CA2022

Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $N A$ groups

Utsav Dewan

We prove a converse of Fatou type result for certain eigenfunctions of the Lalplace-Beltrami operator on Harmonic NA groups relating sectorial convergence and admissible convergenc…

Lost in Translation: Why Lower Bias Scores Don't Mean Fairer Models

Boundary behaviour of eigenfunctions and superharmonic functions on harmonic manifolds of purely exponential volume growth

Cesàro summability of Hölder functions and Talbot effect on rank one Riemannian symmetric spaces of compact type

Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type

Regularity and pointwise convergence for dispersive equations on H2

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces

Iterated convolution inequalities on Rd and Riemannian Symmetric Spaces of non-compact type

Maximal estimates and pointwise convergence for solutions of certain dispersive equations with radial initial data on Damek-Ricci spaces

Pointwise convergence of solutions of the Schrödinger equation along general curves on Damek-Ricci spaces

Mapping properties of the Schrödinger maximal function on Damek--Ricci spaces

Estimates of the Poisson kernel on negatively curved Hadamard manifolds

Regularity and pointwise convergence of solutions of the Schrödinger operator with radial initial data on Damek-Ricci spaces

Restricted Mean Value Property with non-tangential boundary behavior on Riemannian manifolds

Initial singularities of positive solutions of the Heat equation on Stratified Lie groups

Boundary exceptional sets for radial limits of superharmonic functions on non-positively curved Harmonic manifolds of purely exponential volume growth

Restricted mean value property on Riemannian manifolds

Spectral projections and resolvent estimates on Damek-Ricci spaces and their applications

Admissible and sectorial convergence of generalized Poisson integrals on Harmonic NA groups

Regularity and pointwise convergence for dispersive equations on $H^{2}$

Iterated convolution inequalities on $R^{d}$ and Riemannian Symmetric Spaces of non-compact type

Admissible and sectorial convergence of generalized Poisson integrals on Harmonic $N A$ groups