拟微分算子与微局部分析（2025 春）

课程信息

序号	日期	内容	作业 (上课前交)
Lecture 1	03/07	Introduction	hw1: Due March 14
Lecture 2	03/14	Preliminaries, Schwartz space	hw2: Due March 28
Lecture 3	03/21	Tempered distributions, Fourier transform
Lecture 4	03/28	Symbols, ΨDOs and Sobolev spaces
Lecture 5	04/04	No lecture (清明节)	hw3: Due April 25
Lecture 6	04/11	Kernels
Lecture 7	04/16	Oscillatory integrals I
Lecture 8	04/25	Oscillatory integrals II
Lecture 9	05/02	No lecture (五一劳动节)	hw4: Due May 23
Lecture 10	05/09	Stationary phase lemma I
Lecture 11	05/16	Stationary phase lemma II and Symbolic calculus
Lecture 12	05/23	Symbolic calculus and semi-classical ΨDOs
Lecture 13	06/03	Semi-classical ΨDOs and the wavefront set	hw5: Due June 20
Lecture 14	06/06	The wavefront set
Lecture 15	06/13	Propagation of the singularities
Lecture 16	06/20	Q&A
	待定	Final exam

拟微分算子：

M.-W. Wong. An Introduction To Pseudo-differential Operators (3ed). World Scientific Publishing Company, 2014.
陈恕行, 拟微分算子 (第二版). 高等教育出版社, 2006.
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.

微局部分析：

P. Hintz. Microlocal analysis. 2025.
仇庆久陈恕行是嘉鸿刘景麟蒋鲁敏. 傅里叶积分算子理论及其应用. 科学出版社, 1985.
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.