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Solution of the pompeiu problem (i) (2007).
| Content Provider | CiteSeerX |
|---|---|
| Author | Liu, Genqian |
| Abstract | A nonempty bounded open set Ω ⊂ R 2 is said to have the Pompeiu property if and only if the only continuous function f on R 2 for which the integral of f over σ(Ω) is zero for all rigid motions σ of R 2 is f ≡ 0. In this paper, a longstanding open problem, the Pompeiu problem (or equivalently, the Schiffer conjecture), is completely solved in R 2. More precisely, we prove that among bounded open sets of R 2, each of which has a connected Lipschitz boundary, only the disks fail to have the Pompeiu property. In addition, we also give an affirmative answer to a longstanding Morera’s problem. |
| File Format | |
| Publisher Date | 2007-01-01 |
| Access Restriction | Open |
| Subject Keyword | Pompeiu Problem Pompeiu Property Schiffer Conjecture Continuous Function Rigid Motion Lipschitz Boundary Longstanding Morera Problem Bounded Open Set Longstanding Open Problem Open Set Affirmative Answer |
| Content Type | Text |
