This book features a selection of articles by Louis Boutet de Monvel and presents his
contributions to the theory of partial differential equations and analysis. The works selected
here reveal his central role in the development of his field including three cornerstones:
firstly analytic pseudodifferential operators which have become a fundamental aspect of
analytic microlocal analysis and secondly the Boutet de Monvel calculus for boundary problems
for elliptic partial differential operators which is still an important tool also in index
theory. Thirdly Boutet de Monvel was one of the first people to recognize the importance of
the existence of generalized functions whose singularities are concentrated on a single ray in
phase space which led him to make essential contributions to hypoelliptic operators and to a
very successful and influential calculus of Toeplitz operators with applications to spectral
and index theory. Other topics treated here include microlocal analysis star products and
deformation quantization as well as problems in several complex variables index theory and
geometric quantization. This book will appeal to both experts in the field and students who are
new to this subject.
