A necessary and sufficent condition is presented for a set to be a Pompeiu subset of any compact homogeneous space. The condition, which is expressed in terms of the intertwining operators of each primary summand of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds. Examples are presented demonstrating that the condition to be Pompeiu in these...

Let [unk] be a finite family of finite subsets of the n-dimensional lattice Z(n), and let tau denote the group of all translations of Z(n). We shall here consider the Pompeiu problem for the family [unk]-namely, to determine when the only function f:Z(n) --> C such that [Formula: see text] is the zero function.

We consider a two-sided Pompeiu type problem for discrete group G G . give necessary and sufficient conditions finite subset K"> <mml:mi...

In this paper, we combine the fractional ψ − $$ \psi - hyperholomorphic function theory with calculus respect to another function. As a main result, Borel–Pompeiu type formula related Fueter operator vector-valued is proved.