Sundaram Thangavelu

Spherical means and CR functions on the Heisenberg group

The injectivity of the spherical mean value operator on the Heisenberg group is studied. Whenf ∈LP (Hn), 1 ≤p < ∞ it is proved that the spherical mean value operator is injective. When 1 ≤p ≤ 2,f(z, ·) ∈LP (ℝ) the same is proved under much weaker conditions in the z-variable. Some extensions of recent results of Agranovskyet al. regardingCR functions on the Heisenberg group are also obtained.

On regularity of twisted spherical means and special Hermite expansions

Regularity properties of twisted spherical means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localisation theorem for special Hermite expansions.

Summability of Hermite expansions. II

We study the summability of n-dimensional Hermite expansions where n > 1. We prove that the critical index for the Riesz summability is (n - 1)/2. We also prove analogues of the Fejer-Lebesgue theorem and Riemanns localisation principle when the index α of the Riesz means is > (3n - 2)/6.

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

The aim of this paper is to study mean value operators on the reduced Heisenberg group Hn/G, where Hn is the Heisenberg group and G is the subgroup {(0,2pk): k I Z} of Hn.

Some uncertainty inequalities

We prove an uncertainty inequality for the Fourier transform on the Heisenberg group analogous to the classical uncertainty inequality for the Euclidean Fourier transform. Inequalities of similar form are obtained for the Hermite and Laguerre expansions.

An optimal theorem for the spherical maximal operator on the Heisenberg group

AbstractLet

A note on a transplantation theorem of Kanjin and multiple Laguerre expansions

\mathbb{I}^n = \mathbb{C}^n \times \mathbb{R}

Variations on a theorem of cowling and price with applications to nilpotent Lie groups

be the Heisenberg group and μr be the normalized surface measure on the sphere of radiusr in ℂn. Let