Making use of microlocal properties of tempered ultrahyperfunctions corresponding to a convex cone, we give a simple version of the celebrated Edge of the Wedge theorem for this setting.

In the Hyperbolic space Hn (n ≥ 3) there are uncountably many topological types of convex hypersurfaces. When is a locally convex hypersurface in Hn globally convex, that is, when does it bound a convex set? We prove that any locally convex proper embedding of an (n− 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n−1)-flats of the resulting hypersu...

where b, y ∈ IR; ci, xi, si ∈ IRi , Ai ∈ IRm×ni , i = 1, . . . , r. For each i = 1, . . . , r, xi and si are the primal and dual slack variables associated with the ith cone and K∗ i = { si ∈ IRi : xi si ≥ 0, ∀xi ∈ Ki } (3) is the dual cone to Ki. We assume that Ki,K i , i = 1, . . . , r are pointed closed convex cones with nonempty interiors. Let K = K1 × K2 × . . . × Kr be the overall cone in...

A new approach to multispectral and hyperspectral image analysis is presented. This method, called convex cone analysis (CCA), is based on the fact that some physical quantities such as radiance are nonnegative. The vectors formed by discrete radiance spectra are linear combinations of nonnegative components, and they lie inside a nonnegative, convex region. The object of CCA is to find the bou...