- Define Fourier transform and work intensively with it
- Know pseudo-differential operators and their properties and deal with them
- Know first results of Morse theory and apply them to solution operators of differential equations
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Fourier transform, Hermite functions, pseudo-differential operators (definition, asymptotic expansion of the symbol, product, adjoint, parametrix), L^p boundedness of pseudo-differential operators, Sobolev spaces, oscillating integrals, Morse theory
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