We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-
compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the …

An L 2 version of the celebrated Denjoy-Carleman theorem regarding quasi-analytic
functions was proved by Chernoff on R d using iterates of the Laplacian. In 1934 Ingham …

In this article we study the Fourier and the horocyclic Radon transform on harmonic $ NA $
groups (also known as Damek-Ricci spaces). We consider the geometric Fourier transform …

In this paper, we prove an analog of Younis's result Int J Math Math Sci 9 (2): 301–312 1986,
Theorem 5.2 on the image under the Fourier–Helgason transform of a set of functions …

In a recent paper by the authors, growth properties of the Fourier transform on Euclidean
space and the Helgason Fourier transform on rank one symmetric spaces of non-compact …

In this paper we prove a new inversion theorem and a refinement of an old support theorem
for two Radon transforms on a symmetric space. Included are some new identities for the …

We shall obtain inequalities for Fourier transform via moduli of continuity on NA groups.
These results in particular settle the conjecture posed in a recent paper by WO Bray and M …

Abstract We prove a Wiener Tauberian theorem for the L 1 spherical functions on a
semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for …

We will show that an uniform treatment yields Wiener–Tauberian type results for various
Banach algebras and modules consisting of radial sections of some homogenous vector …

We show various uncertainty principles for the Fourier transform on harmonic manifolds of
rank one. In particular, we derive a Heisenberg uncertainty principle, a Morgen theorem, an …