Continuous functions with compact support

Continuous Functions on Compact Groups

We show that every scalar valued continuous function f(g) on a compact group G may be written as f(g) = 〈Φ(g)ξ, η〉 for all g ∈ G, where ξ, η are vectors in a separable Hilbert space H, and Φ(g) is a strongly continuous unitary valued function on G which is a product of unitary representations and antirepresentations of G on H. This product is countable, but always converges uniformly on G. More...

Characterizing Continuous Functions on Compact Spaces

We consider the following problem: given a set X and a function T : X → X, does there exist a compact Hausdorff topology on X which makes T continuous? We characterize such functions in terms of their orbit structure. Given the generality of the problem, the characterization turns out to be surprisingly simple and elegant. Amongst other results, we also characterize homeomorphisms on compact me...

Hölder Continuous Solutions of Boussinesq Equation with Compact Support

Here e2 = (0, 1) T , v is the velocity vector, p is the pressure, θ is a scalar function. The Boussinesq equations arises from many geophysical flows, such as atmospheric fronts and ocean circulations (see, for example, [25],[27]). To understand the turbulence phenomena in fluid mechanics, one needs to go beyond classical solutions. The pair (v, p, θ) on R2×R is called a weak solution of (1.1) ...

On images of continuous functions from a compact manifold to Euclidean space

A new class of radial basis functions with compact support

Radial basis functions are well-known and successful tools for the interpolation of data in many dimensions. Several radial basis functions of compact support that give rise to nonsingular interpolation problems have been proposed, and in this paper we study a new, larger class of smooth radial functions of compact support which contains other compactly supported ones that were proposed earlier...