منابع مشابه
Radon transforms and packings
We use some basic results and ideas from the integral geometry to study certain properties of group codes. The properties being studied are generalized weights and spectra of linear block codes over a finite field and their analogues for lattice sphere packings in Euclidean space. We do not obtain any new results about linear codes, although several short and simple proofs for known results are...
متن کاملEstimates for Generalized Radon Transforms
Sobolev and L p ? L q estimates for degenerate Fourier integral operators with fold and cusp singularities are discussed. The results for folds yield sharp estimates for restricted X-ray transforms and averages over non-degenerate curves in R 3 and those for cusps give sharp L 2 estimates for restricted X-ray transforms in R 4. In R 4 , sharp Lebesgue space estimates are proven for a class of m...
متن کاملRadon Transforms on Affine Grassmannians
We develop an analytic approach to the Radon transform f̂(ζ) = ∫ τ⊂ζ f(τ), where f(τ) is a function on the affine Grassmann manifold G(n, k) of k-dimensional planes in Rn, and ζ is a k′-dimensional plane in the similar manifold G(n, k′), k′ > k. For f ∈ Lp(G(n, k)), we prove that this transform is finite almost everywhere on G(n, k′) if and only if 1 ≤ p < (n− k)/(k′− k), and obtain explicit inv...
متن کاملEstimates for Overdetermined Radon Transforms
We prove several variations on the results in Ricci and Travaglini[RT] concerning L−L ′ bounds for convolution with all rotations of a measure supported by a fixed convex curve in R. Estimates are obtained for averages over higherdimensional convex (nonsmooth) hypersurfaces, smooth k-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare the approach of [RT], based ...
متن کاملReconstructions from Doppler Radon transforms
We will study whether it is possible to regain information about a vector eld from projections, in the same way as is possible for scalar functions with Radon transform. It turns out that the curl and divergence of the eld can be reconstructed separately from two different transforms, and algorithms are devised using a variant of the ltered back projection algorithm for reconstruction. It is a ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1980
ISSN: 0001-8708
DOI: 10.1016/0001-8708(80)90058-4