Mathematical Sciences: Oscillatory Integrals, Singular Integrals, and Their Applications

点击翻译按钮获取中文摘要

Abstract: Pan Pan's investigation will be focused on various singular integral and oscillatory integral operators which arise naturally in many problems in harmonic analysis and related fields including complex analysis and the theory of partial differential equations. With applications to a large number of problems in mathematics, these integrals have received an increasing amount of recognition for their importance. While research in this area has been intensive and fruitful, much more remains to be understood. This project will cover many topics of current interest, which when finished will make a big stride toward the full understanding of these operators and related problems in mathematical analysis. The objects under investigation form an important part of the mathematical modeling of physical phenomena such as heat conducting and wave motion. They also appear in engineering problems involving electric circuits and signal processing. Thus, gaining understanding of such objects will not only have theoretical values but also provide guidance in other areas of science and engineering.