microlocal analysis

In mathematical analysis, microlocal analysis is a term use to describe techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes generalized functions, pseudo-differential operators, wave front sets, Fourier integral operators, and paradifferential operators.

The term microlocal implies localisation not just at a point, but in terms of cotangent space directions at a given point. This gains in importance on manifolds of dimension greater than one.

This entry was adapted from the Wikipedia article http://en.wikipedia.org/wiki/Microlocal_analysisMicrolocal analysis as of January 17, 2007.