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
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.
Victor Guillemin was born in Cambridge, Massachusetts in 1937, obtained his Ph.D
degree in Mathematics at Harvard in 1962, and has been a member of the MIT
Mathematics Department since 1967. His area of expertise is symplectic
geometry, semi-classical analysis and linear partial differential equations.
Johannes Sjöstrand was born in Gothenburg, Sweden in 1947, obtained his PhD degree in Mathematics at the University in Lund in 1972, he has spent most of his professional career in France (Paris, Nice, Orsay, Palaiseau and more recently at the Universite de Bourgogne in Dijon). He works in partial differential equations and spectral theory with tools from microlocal and occasionally complex analysis.
Introduction.- Biography.- Commentary by B. Malgrange.- Elliptic boundary problems.- Analytic pseudodifferential operators.- Operators with double characteristics.-
6Bergman and Szegö kernels, CR analysis.- Toeplitz operators.- Star products
and deformation quantization.- Miscellaneous.- Acknowledgements.- Addresses