Multiplications on the Space of Probability Distribution Functions.
We define a category containing the discrete quantum groups (and hence the discrete groups and the duals of compact groups) and the compact quantum groups (and hence the compact groups and the duals of discrete groups). The dual of an object can be defined within the same category and we have a biduality theorem. This theory extends the duality between compact quantum groups and discrete quantum groups (and hence the one between compact abelian groups and discrete abelian groups). The objects in...
A multiresolution analysis is defined in a class of locally compact abelian groups . It is shown that the spaces of integrable functions and the complex Radon measures admit a simple characterization in terms of this multiresolution analysis.
[For the entire collection see Zbl 0742.00067.]This paper is devoted to a method permitting to determine explicitly all multilinear natural operators between vector-valued differential forms and between sections of several other natural vector bundles.
For an abelian lattice ordered group let be the system of all compatible convergences on ; this system is a meet semilattice but in general it fails to be a lattice. Let be the convergence on which is generated by the set of all nearly disjoint sequences in , and let be any element of . In the present paper we prove that the join does exist in .