TY - JOUR
T1 - Uniqueness theorems for Fourier transforms
AU - Lev, Nir
N1 - Funding Information: The latter condition implies, however, that if ν is non-zero then the closed support of ν is a set of infinite 1-dimensional Hausdorff measure (see [2, pp. 132–134]). But this is not possible since ν is supported by the image of the curve Γ under the projection R2 → T2. Hence ν = 0.
PY - 2011/3
Y1 - 2011/3
N2 - Let Γ be a smooth curve in the plane R2, and μ be any subset of R2. When can one recover uniquely a finite measure Γ supported by Γ and absolutely continuous with respect to the arc length measure on Λ from the restriction to Λof 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 Γ is "close" to a lattice.
AB - Let Γ be a smooth curve in the plane R2, and μ be any subset of R2. When can one recover uniquely a finite measure Γ supported by Γ and absolutely continuous with respect to the arc length measure on Λ from the restriction to Λof 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 Γ is "close" to a lattice.
UR - http://www.scopus.com/inward/record.url?scp=79651468706&partnerID=8YFLogxK
U2 - 10.1016/j.bulsci.2010.12.002
DO - 10.1016/j.bulsci.2010.12.002
M3 - مقالة
SN - 0007-4497
VL - 135
SP - 134
EP - 140
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
IS - 2
ER -