7 papers · 1 filter
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 ), we first obtain a quantitative characterization of Hölder continuity in terms of Cesàro means. In ad…
Regularity and pointwise convergence for dispersive equations on
Utsav Dewan
In the prototypical setting of non-Euclidean geometry, the 2-dimensional Real Hyperbolic space , we consider the Carleson's problem for the Schrödinger equation and i…
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 of the Schrödinger equ…
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 . Recently, the author along with…
Initial singularities of positive solutions of the Heat equation on Stratified Lie groups
Utsav Dewan
Let be a stratified Lie group. We estimate the Hausdorff dimension (with respect to the Carnot-Carathéodory metric) of the singular sets in , where…
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…
Admissible and sectorial convergence of generalized Poisson integrals on Harmonic 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…