Uniqueness theorems for Fourier transforms

✍ Scribed by Nir Lev

• Publisher: Elsevier Science
• Year: 2011
• Tongue: French
• Weight: 94 KB
• Volume: 135
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/j.bulsci.2010.12.002

✦ Synopsis

Let Γ be a smooth curve in the plane R 2 , and Λ be any subset of R 2 . When can one recover uniquely a finite measure μ, supported by Γ and absolutely continuous with respect to the arc length measure on Γ , from the restriction to Λ of its Fourier transform? In this note we present two results in the subject, one is concerned with the case when Γ is a circle, and the other with the case when Λ is "close" to a lattice.