On Semiclassical Operators: Semiclassical Analysis

Student thesis: Master thesis (including HD thesis)

  • Kristian Lundgaard Kjøller
  • Tróndur Tummasarson Johannesen
4. term, Mathematics, Master (Master Programme)
In this Master’s thesis we study some results from semiclassical analysis. First we give the meaning to the anti-Wick quantization for a classical pseudodifferential operator and then extend this to semiclassical case. We utilize this to prove Gårding’s inequality. Thereafter, we give a formula for the Fourier transform of eicxm, when m is even, which for m > 2 involves generalized hypergeometric functions. Lastly, we study oscillatory integrals, especially their behaviour when h goes to 0. This leads us to study stationary phase asymptotics, under different conditions, where we among other things have tried to use the aforementioned Fourier transform. In higher dimensions this required us to show Morse Lemma.
Publication date7 Jun 2018
Number of pages42
ID: 280522851