Pompeiu sets in compact Heisenberg manifolds

Document Type

Article

Publication Date

1-1-2000

Abstract

A necessary and sufficient condition is presented for a set to be a Pompeiu subset of any compact homogeneous space with a finite invariant measure. 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 manifold's. Examples are presented demonstrating that the condition to be Pompeiu in these manifolds is quite different from the corresponding condition for a torus of the same dimension. This provides a contrast with the existing comparison between the Heisenberg group itself and Euclidean space in terms of Pompeiu sets. In addition, the closed linear span of all translates of any square integrable function on any compact homogeneous space is determined. © 2000 Birkhäuser Boston. All rights reserved.

Publication Source (Journal or Book title)

Journal of Fourier Analysis and Applications

First Page

43

Last Page

54

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