Spaces of symbols (somewhat more general than these) will play an important r^ole below and are a very important component of the microlocal analysis of distributions.

Volume I. Semiclassical Microlocal Analysis and Local and Microlocal Semiclassical Asymp- totics1.

study of the singularities of solu-tions of PDEs. Unlike local analysis, which is concerned with the regularity of distributions near points of particular interest, microlocal analysis is concerned …

This text, publishing in the high profile, Graduate Texts in Mathematics series, presents a classical topic, microlocal analysis and pseudodifferential operators, with an eye toward modern …

Microlocal analysis, loosely speaking, is analysis near points and directions, i.e., in the \phase space". We review here brie y the theory of pseudo-di erential operators, and geometrical op-tics.

Mar 22, 2023 · To accommodate an intuitive notion of a “function of differential operators” there is a simple trick used: consider the Fourier transform. Then the differential operators become …

Microlocal analysis studies singularities of distributions in phase space, by describing the behaviour of the singularity in both position and direction. It is a part of the eld of partial di …