On Non-abelian Radon Transform. *
نویسنده
چکیده
We consider the inverse prolem of the recovery of a gauge field in R 2 modulo gauge transformations from the non-abelian Radon transform. A global uniqueness theorem is proven for the case when the gauge field has a compact support. Extensions to the attenuated non-abelian Radon transform in R 2 and applications to the inverse scattering problem for the Schrödinger equation in R 2 with non-compact Yang-Mills potentials are studied.
منابع مشابه
Truncated Counting Functions of Holomorphic Curves in Abelian Varieties
A new proof of the Second Main Theorem with truncation level 1 for Zariski-dense holomorphic curves into Abelian varieties, which has just been proved by Yamanoi [Y2], is presented. Our proof is based on the idea of the “Radon transform” introduced in [K2] combined with consideration on certain singular perturbation of the probability measures on the parameter space which appears in the “Radon ...
متن کاملThe Radon transform on Abelian Groups
The Radon transform on a group A is a linear operator on the space of functions /: A-+ C. It is shown that if A = Z;: then the Radon transform with respect to a subset B c .4 is not invertible if and only if B has the same number of elements in every coset of some maximal subgroup of A. The same does not hold in general for arbitrary finite abelian groups. ' IW7 ACxhlK I%\\. 1°C Let A be a fini...
متن کاملOn Functions Which Are Fourier Transforms
1. Let G be a locally compact and abelian group, Gl the dual group. Through this paper, "Ml will denote the set of all bounded Radon measure n on G; this set will be considered as a Banach algebra when provided with the customary norm as the dual of the space Co(G) defined below and with the ring product defined as convolution. If /iGM1, its Fourier transform is by definition the bounded and co...
متن کامل3D Fourier based discrete Radon transform
The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Recently A. Averbuch et al. [SIAM J. Sci. Comput., submitted for publication] developed a coherent discrete definition of the 2D discrete Radon transform for 2D discrete images. The definition in [SIAM J. Sci. Comput., submitted for publication] is shown to be ...
متن کاملWavelets and Local Tomography
In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi{continuous wavelet transform of Mallat, steerable multiscale lters of Freeman and Adelson, and separable orthogonal and non{orthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the loc...
متن کامل