D-modules and Microlocal Calculus

ISBN-13: 9780821827666 / Angielski / Miękka / 2002 / 254 str.

Masaki Kashiwara

Opis

The theory of $D$-modules is powerful, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. which were obtained by the author. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. A hot topic from the mid 1970s to mid 1980s, it has now moved a bit more into the mainstream, and graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a solid perspective for presenting the topic to the general mathematical public.