Uniqueness theorems for Fourier transforms

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 t...

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Bibliographic Details
Published inBulletin des sciences mathématiques Vol. 135; no. 2; pp. 134 - 140
Main Author Lev, Nir
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier SAS 01.03.2011
Elsevier
Subjects
Combinatorics. Ordered structures
Exact sciences and technology
General mathematics
General, history and biography
Mathematics
Order, lattices, ordered algebraic structures
Sciences and techniques of general use
Circle
Fourier transformation
Support
Arc length
Uniqueness theorem
Lattice
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Summary: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.
ISSN:0007-4497
1952-4773
DOI:10.1016/j.bulsci.2010.12.002