By Jan-Erik Björk
This is often the 1st monograph to be released on analytic D-modules and it bargains a whole and systematic remedy of the rules including a radical dialogue of such smooth subject matters because the Riemann--Hilbert correspondence, Bernstein--Sata polynomials and a wide number of effects referring to microdifferential research. Analytic D-module idea reviews holomorphic differential structures on complicated manifolds. It brings new perception and strategies into many parts, corresponding to limitless dimensional representations of Lie teams, asymptotic expansions of hypergeometric capabilities, intersection cohomology on Kahler manifolds and the calculus of residues in numerous complicated variables. The publication comprises seven chapters and has an intensive appendix that is dedicated to crucial instruments that are utilized in D-module thought. This comprises an account of sheaf concept within the context of derived different types, an in depth research of filtered non-commutative jewelry and homological algebra, and the fundamental fabric in symplectic geometry and stratifications on advanced analytic units. For graduate scholars and researchers.