Stable laws and Beurling kernels

We identify a close relation between stable distributions and the limiting homomorphisms central to the theory of regular variation. In so doing some simplifications are achieved in the direct analysis of these laws in Pitman and Pitman [PitP]; stable distributions are themselves linked to homomorphy

Colimits in the correspondence bicategory

We interpret several constructions with C*-algebras as colimits in the bicategory of correspondences. This includes crossed products for actions of groups and crossed modules, Cuntz-Pimsner algebras of proper product systems, direct sums and inductive limits, and certain amalgamated free products.Comment: Final versio

Simplifications of Homomorphisms ; CU-CS-114-77

The notion of a simplification of a homomorphism is introduced and investigated. Its usefulness is demonstrated in providing rather short proofs of the following results: (i) Given an arbitrary homomorphism h and arbitrary words x, y it is decidable whether or not there exists an integer n such that h^n(x) = h^n(y). (ii) Given an arbitrary homomorphism h and arbitrary words x, y it is decidable whether or not there exists integers n and r such that h^n(x) = h^r(y) (iii) Given an arbitrary DOL system G and an arbitrary integer d it is decidable whether or not G is locally caternative of depth not larger than d. (iv) The equivalence problem for elementary polynomially bounded DOL systems is decidable

A short proof of the Buchstaber-Rees theorem

We give a short proof of the Buchstaber-Rees theorem concerning symmetric powers. The proof is based on the notion of a formal characteristic function of a linear map of algebras.Comment: 11 pages. LaTeX2