Radon transforms and finite type conditions
نویسندگان
چکیده
منابع مشابه
Radon Transforms and Finite Type Conditions
The purpose of this paper is to study averaging operators of Radon transform type. We shall formulate suitable finite type conditions and prove L-Sobolev and L → L estimates. The results will be essentially sharp for operators associated with families of curves in the plane. Let X and Y be smooth manifolds, dimX = nL, dim Y = nR, and let M be a submanifold in X×Y with conormal bundle N∗M; we de...
متن کاملRadon Transforms and the Finite General Linear Groups
Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approach is analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used...
متن کاملRadon 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 کاملGeneralized Transforms of Radon Type and Their Applications
These notes represent an extended version of the contents of the third lecture delivered at the AMS Short Course “Radon Transform and Applications to Inverse Problems” in Atlanta in January 2005. They contain a brief description of properties of some generalized Radon transforms arising in inverse problems. Here by generalized Radon transforms we mean transforms that involve integrations over c...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1998
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-98-00280-x