Cohomological Laplace Transform on Non-convex Cones and Hardy Spaces of (partial derivative)over-bar-cohomology on Non-convex Tube Domains

摘要

We consider a class of non-convex cones V in R-n which can be presented as (not unique) union of convex cones of some codimension q which we call the index of non-convexity. This class contains non-convex symmetric homogeneous cones studied in D'Atri-Gindikin ([DAG93]) and Faraut-Gindikin ([FaGi96]). For these cones we consider a construction of dual non-convex cones V* and corresponding non-convex tubes T and define a cohomological Laplace transform from functions at V to q-dimensional cohomology of T using the language of smoothly parameterized Cech cohomology. We give a construction of Hardy space of q-dimensional cohomolgy at T.