Mathematical Sciences: Sampling Solutions of Ill-Posed Problems

点击翻译按钮获取中文摘要

This project will develop numerical methods for the solution of ill-posed integral and operator equations. The methods are based on a new general approach to sampling theorems for functions in reproducing kernel subspaces of a Sobolev space. Various types of errors (truncation, aliasing, jitter, and amplitude) will be studied. Sampling theory for regular Mikusinski operators as well as wavelet sampling of ill- posed problems will be initiated. This project is motivated by several applications arising in subjects ranging from radar technology to oil recovery. These studies are part of the foundation of software development in applications such as scanning and tomography