Hoermander operators are a class of linear second order partial
differential operators with nonnegative characteristic form and
smooth coefficients, which are usually degenerate
elliptic-parabolic, but nevertheless hypoelliptic, that is highly
regularizing. The study of these operators began with the 1967
fundamental paper by Lars Hoermander and is intimately connected to
the geometry of vector fields.Motivations for the study of
Hoermander operators come for instance from
Kolmogorov-Fokker-Planck equations arising from modeling physical
systems governed by stochastic equations and the geometric theory
of several complex variables. The aim of this book is to give a
systematic exposition of a relevant part of the theory of
Hoermander operators and vector fields, together with the necessary
background and prerequisites.The book is intended for self-study,
or as a reference book, and can be useful to both younger and
senior researchers, already working in this area or aiming to
approach it.
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