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MATS5110 Topics in harmonic analysis:
pseudodifferential operators and microlocal analysis (2021)

• Course page in SISU
• Instructor: Shiqi Ma, MaD303, JYU

Lecture notes,  (updated: 14/11/2021)

This course focuses on pseudodifferential operators and microlocal analysis,
including topics such as stationary phase lemma, symbolic calculus and computation of wavefront sets.

Some good references

For the pseudodifferential operators,

• M.-W. Wong. An Introduction To Pseudo-differential Operators (3ed). World Scientific Publishing Company, 2014.
• S. Alinhac, P. Gérard. Pseudo-differential operators and the Nash-Moser theorem. American Mathematical Soc., 2007.
• M. Zworski. Semiclassical analysis. Vol. 138. American Mathematical Soc., 2012.
• M. S. Joshi. Introduction to Pseudo-differential Operators. arXiv:math.AP/9906155, 1999. link
• 陈恕行. 拟微分算子. 高等教育出版社, 2006. (in Chinese)

• A. Grigis, J. Sjöstrand. Microlocal analysis for differential operators: an introduction. Cambridge University Press, 1994.
• L. Hörmander. The analysis of linear partial differential operators III: Pseudo-differential operators. Springer, 2007.
• C. D Sogge. Fourier integrals in classical analysis. Vol. 210. Cambridge University Press, 2017.
• F. Treves. Introduction to Pseudodifferential and Fourier Integral Operators. Vol. 1-2, 1980-1982.
• J. Wunsch. Microlocal analysis and evolution equations. arXiv:0812.3181, 2008.
• P. Hintz. Introduction to microlocal analysis.

Exercises

The exercises will be discussed in the exercise session three weeks after the corresponding lectures.
All the exercises must be returned to Leyter Potenciano, by email, in three weeks before the exercise session.

Passing the course

The course is graded as pass/fail without a numerical grade. Passing requires the following:

• Returning exercises electronically by email.
• Returning at least two third (2/3) of all exercises by Monday May 31.