The extremal structure of locally compact convex sets

A convex combinatorial property of compact sets in the plane and its roots in lattice theory

K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...

Pseudoframe multiresolution structure on abelian locally compact groups

‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

Directed Sets and Diierences of Convex Compact Sets 3

Spline Subdivision Schemes for Convex Compact Sets

The application of spline subdivision schemes to data consisting of convex compact sets with addition replaced by Minkowski sums of sets is investigated These methods generate in the limit set valued functions which can be expressed explicitly in terms of linear com binations of integer shifts of B splines with the initial data as coe cients The subdivision techniques are used to conclude that ...

Classifying compact convex sets with frames

Classification is a fundamental image processing task. Recent empirical evidence suggests that classification algorithms which make use of redundant linear transforms will regularly outperform their nonredundant counterparts. We provide a rigorous explanation of this phenomenon in the single-class case. We begin by developing a measure-theoretic analysis of the set of points at which a given de...