Recent years have seen much effort put into attempts to develop an "abstract" function theory. In the complex domain, this has led to the study of the structure of uniform algebras. A uniform algebra 31 is a family of continuous complex-valued functions on a compact Hausdorff space X, which contains the function 1, which is closed with respect to the algebraic operations of addition and multipl...

In this survey article, we will introduce various measures of complexity for algebraic constructions in polynomial rings over fields and show how they are often uniformly bounded by the complexity of the starting data. In problems which have a linear nature, the degree of the polynomials provide a sufficient notion of complexity. However, in the non-linear case, the more sophisticated measure o...

Spaces of all entire functions f represented by vector valued Dirichlet series and having slow growth have been considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous transformations is characterized. Proper bases have also been characterized in terms of growth parameters.

The uniform Roe C U G . The reduced C algebra C G is naturally contained in CU G . We show that the elements of l∞ which are invariant under are of the form l∞ . Finally we show that if and are bounded geometry discrete metric spaces, then

This work presents a methodological framework suitable for the design of innovative sym bolic computation systems A signi cant set of basic algebraic structures is de ned and implemented by a uniform representation based on the algebraic structure of truncated power series By following this approach we succeed in avoiding the need for explicit coercion in computing with the de ned structures We...

We prove something.

We show that every nonvoid relatively weakly open subset, in particular every slice, of the unit ball of an infinite-dimensional uniform algebra has diameter 2. It is an important task in Banach space theory to determine the extreme point structure of the unit ball for various examples of Banach spaces. The most common way to describe “corners” of convex sets is by looking for extreme points, e...