Microlocal Analysis and Precise Spectral Asymptotics

Focusing on spectral asymptotics, this work delves into the distribution of eigenvalues in the context of partial differential operators, a crucial aspect of spectral theory. The author began research in 1979 inspired by significant findings from R. Seeley, M. Shubin, and B. M. Levitan. Despite challenges in 1985 that led to doubts about progress, a pivot towards local semiclassical spectral asymptotics and rescaling revitalized the research, unveiling new possibilities in the field.