The Heisenberg group plays an important role in several branches of mathematics, such as
representation theory, partial differential equations, number theory, several complex …

Integral geometry deals with the problem of determining functions by their integrals over
given families of sets. These integrals define the corresponding integral transform and one …

A necessary and sufficient characterization is given that specifies which sets of sums of
translations of radial functions are dense in the set of continuous functions in the plane. This …

The injectivity of the spherical mean value operator on the Heisenberg group is studied.
When f∈ LP (H n), 1≤ p<∞ it is proved that the spherical mean value operator is injective …

Let E be a bounded Borel subset of ℝ n, n≥ 2, of positive Lebesgue measure and PE the
corresponding 'Pompeiu transform”. We prove that PE is injective on L p (ℝ n) if 1≤ p≤ 2 …

In the case ofR71, it was proved by Brown et al in [4] that if V c C (Rn) is a closed subspace
invariant under translations and rotations then V contains a function^{x)=(AI^ D^-^^ AM) for …

We establish injectivity results for three different spherical means on an H-type group, G. The
first one is the standard spherical mean operator, which is defined as the average of a …

A short and self-contained presentation of the results known about the Pompeiu problem is
given and result is obtained. In particular, it is proved that if D1 has Pompeiu's property (P …

In this paper we prove that cylinders of the form ΓR= SR× R, where SR is the sphere {z∈ C
n:| z|= R}, are injectivity sets for the spherical mean value operator on the Heisenberg group …

The classical theorem of Morera characterizes holomorphic functions of one complex
variable in terms of integral conditions, eg, a continuous function/in the unit disk D is …