The pompeiu problem

Abstract

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-property) then D₂ has it, provided D₂ is sufficiently close to D₁ in the following sense: meas (D₁₂\D¹²) is sufficiently small. Here D₁₂ = D₁ ∪ D₂ D¹² = D₁ D₂ .

Keywords:

• Pompeiu Problem
• Inverse Problems
• Meta Hormonic Potentials