5 papers · 1 filter
Boundary behaviour of eigenfunctions and superharmonic functions on harmonic manifolds of purely exponential volume growth
Utsav Dewan
On , a non-positively curved harmonic manifold of purely exponential volume growth, of dimension , we study certain quantitative aspects of the boundary behavi…
Iterated convolution inequalities on 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 on and proved that the real integra…
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 of the Schrödinger equ…
Mapping properties of the Schrödinger maximal function on Damek--Ricci spaces
Utsav Dewan, Swagato K. Ray
For , the collection of radial -Schwartz class functions on Damek--Ricci spaces , we consider the Schrödinger maximal function…
Spectral projections and resolvent estimates on Damek-Ricci spaces and their applications
Mithun Bhowmik, Utsav Dewan
We prove 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…