Application of methods of harmonic analysis

Princeton University, Princeton NJ

Investigators

Abstract

Abstract Fefferman and Stein will study problems in harmonic analysis, including the decay of multilinear-operator-valued oscillatory integrals, the domination of pseudodifferential operators, ergodic theory on semisimple Lie groups, multi-parameter harmonic analysis and its applications to several complex variables, constructive methods in fluid mechanics, discrete versions of singular Radon transforms, scaling laws for mechanical systems, and applications of harmonic analysis to atoms. Harmonic analysis began with the work of Fourier in the early 19th century. Its theme is to analyze complex behavior (heat flow, vibration,...) by writing it as a sum of basic pieces behaving in the simplest way. Harmonic analysis is crucial in many parts of science and technology. Fefferman and Stein are pursuing ideas in harmonic analysis and relating them to problems in mathematics and physics.