Swagato K. Ray

Uncertainty principles like Hardy's theorem on some Lie groups

We extend an uncertainty principle due to Cowling and Price to Euclidean spaces, Heisenberg groups and the Euclidean motion group of the plane. This uncertainty principle is a generalisation of a classical result due to Hardy. We also show that on the real line this uncertainty principle is almost equivalent to Hardys theorem.

FOURIER AND RADON TRANSFORM ON HARMONIC NA GROUPS

In this article we study the Fourier and the horocyclic Radon transform on harmonic N A groups (also known as Damek-Ricci spaces). We consider the geometric Fourier transform for functions on L p -spaces and prove an analogue of the L 2 -restriction theorem. We also prove some mixed norm estimates for the Fourier transform generalizing the Hausdorff-Young and Hardy-Littlewood-Paley inequalities. Unlike Euclidean spaces the domains of the Fourier transforms are various strips in the complex plane. All the theorems are considered on these entire domains of the Fourier transforms. Finally we deal with the existence of the Radon transform on L P -spaces and obtain its continuity property.

The Helgason-Fourier Transform for Symmetric Spaces II

We formulate analogues of the Hausdor-Young and Hardy- Littlewood-Paley inequalities, the Wiener Tauberian theorem, and some un- certainty theorems on Riemannian symmetric spaces of noncompact type using the Helgason-Fourier transform.

Cowling-Price theorem and characterization of heat kernel on symmetric spaces

We extend the uncertainty principle, the Cowling-Price theorem, on noncompact Riemannian symmetric spacesX. We establish a characterization of the heat kernel of the Laplace-Beltrami operator onX from integral estimates of the Cowling-Price type.

Uncertainty principles on two step nilpotent Lie groups

We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.

A theorem of Beurling and Hörmander on Damek–Ricci spaces

Abstract We prove Beurlings theorem and Lp –Lq Morgans theorem for Damek–Ricci spaces. These two theorems exhaust a family of theorems which illustrate a well-known paradigm that a function and its Fourier transform cannot be simultaneously localized.