arXiv subjects
Publications and source records attributed to Jeremy J. Becnel.
The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.
Here we present an overview of countably-normed spaces. We discuss the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and discuss the sigma-fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the sigma-fields generated by the weak, strong, and inductive topologies are equal. With these sigma-fields, we develop a Gaussian measure on the dual of a nuclear space. The purpose in mind is to provide the background material for many of the results used is White Noise Analysis.