Microlocal analysis and evolution equations
Jared Wunsch
TL;DR
This paper provides an informal introduction to microlocal analysis techniques and their applications in studying linear evolution equations and spectral theory, emphasizing practical application over rigorous construction.
Contribution
It offers an overview of pseudodifferential and Fourier integral operators, focusing on their application in evolution equations without detailed construction.
Findings
Illustrates how microlocal methods apply to evolution equations
Highlights the use of pseudodifferential and Fourier integral operators
Provides practical insights into spectral theory applications
Abstract
Lecture notes from 2008 CMI/ETH Summer School on Evolution Equations. These notes are an informal introduction to the applications of microlocal methods in the study of linear evolution equations and spectral theory. Calculi of pseudodifferential operators and Fourier integral operators are discussed and axiomatized, but not constructed: the focus is on how to apply these tools.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Advanced Harmonic Analysis Research · Numerical methods in inverse problems