Microlocal and Macrolocal Analysis - Patrik WAHLBERG - Politecnico di Torino

The talk is a survey of certain parts of microlocal analysis, from the point of view of the short-time Fourier transform (STFT). The STFT manifests various versions of the Uncertainty Principle. We discuss the (smooth) wavefront set as a limit of information from the STFT, with perfect localization in the variable but only directional localization in the covariable. Then we take a global point of view of the STFT and discuss function spaces and wavefront sets defined in terms of the STFT. They encode smoothness and decay comprehensively. Finally we givesome applications to linear evolution PDEs.

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