Support Theorems for the Radon Transform and Cramér-Wold Theorems
نویسندگان
چکیده
منابع مشابه
Support theorems for the Radon transform and Cramér-Wold theorems
This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distri...
متن کاملNew Range Theorems for the Dual Radon Transform
Three new range theorems are established for the dual Radon transform R∗: on C∞ functions that do not decay fast at infinity (and admit an asymptotic expansion), on S(Zn), and on C∞ 0 (Zn). Here Zn := Sn−1×R, and R∗ acts on even functions μ(α, p) = μ(−α,−p), (α, p) ∈ Zn.
متن کاملLusin type theorems for Radon measures
We add to the literature the following observation. If μ is a singular measure on R which assigns measure zero to every porous set and f : R → R is a Lipschitz function which is non-differentiable μ-a.e., then for every C function g : R → R it holds μ{x ∈ Rn : f(x) = g(x)} = 0. In other words the Lusin type approximation property of Lipschitz functions with C functions does not hold with respec...
متن کاملPaley–wiener Theorems for the Dunkl Transform
We conjecture a geometrical form of the Paley–Wiener theorem for the Dunkl transform and prove three instances thereof, by using a reduction to the one-dimensional even case, shift operators, and a limit transition from Opdam’s results for the graded Hecke algebra, respectively. These Paley– Wiener theorems are used to extend Dunkl’s intertwining operator to arbitrary smooth functions. Furtherm...
متن کاملThe Zak transform and sampling theorems for wavelet subspaces
The Zak transform is used for generalizing a sampling theorem of G. Walter for wavelet subspaces. Cardinal series based on signal samples f(a + n), n E 2 with a possibly unequal to 0 (Walter’s case) are considered. The condition number of the sampling operator and worst-case aliasing errors are expressed in terms of Zak transforms of scaling function and wavelet. This shows that the stability o...
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 Theoretical Probability
سال: 2008
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-008-0151-0