Smooth and Polyhedral Norms via Fundamental Biorthogonal Systems

Fundamental Re nable Functions , Duals and Biorthogonal

In areas of geometric modeling and wavelets, one often needs to construct a compactly supported reenable function with suucient regularity which is fundamental for interpolation (that means, (0) = 1 and () = 0 for all 2 Z s nf0g). Low regularity examples of such functions have been obtained numerically by several authors and a more general numerical scheme was given in RiS1]. This paper present...

Intersection Properties of Polyhedral Norms

We investigate the familyM of intersections of balls in a finite dimensional vector space with a polyhedral norm. The spaces for whichM is closed under Minkowski addition are completely determined. We characterize also the polyhedral norms for which M is closed under adding a ball. A subset P ofM consists of the Mazur sets K, defined by the property that for any hyperplane H not meeting K there...

Biorthogonal Smooth Local Trigonometric Bases

In this paper we discuss smooth local trigonometric bases. We present two generalizations of the orthogonal basis of Malvar and Coifman-Meyer: biorthogonal and equal parity bases. These allow natural representations of constant and, sometimes, linear components. We study and compare their approximation properties and applicability in data compression. This is illustrated with numerical examples.

Polytopes Related to Some Polyhedral Norms. Polytopes Related to Some Polyhedral Norms

Finite and Infinitesimal Rigidity with Polyhedral Norms

We characterise finite and infinitesimal rigidity for bar-joint frameworks in R with respect to polyhedral norms (i.e. norms with closed unit ball P a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in R which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of ...