This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015.

The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover...