Unbounded visibility domains, the end compactification, and applications

Bounded Domains and Unbounded Domains

First, notions of inside components and outside components are introduced for any subset of n-dimensional Euclid space. Next, notions of the bounded domain and the unbounded domain are defined using the above components. If the dimension is larger than 1, and if a subset is bounded, a unbounded domain of the subset coincides with an outside component (which is unique) of the subset. For a spher...

SOLVING SINGULAR ODES IN UNBOUNDED DOMAINS WITH SINC-COLLOCATION METHOD

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

Directed rectangle visibility graphs have unbounded dimension

Hyperbolicity in Unbounded Convex Domains

We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.

Problems in Unbounded Cylindrical Domains

We combine the classical point of view of special functions with functional calculus for sectorial operators to obtain semi-explicit representation formulæ for the solutions.The formulæ are well suited for the further study of their properties as well as for the precise characterization of asymptotic behaviour in the large or for vanishing parameters (such as in perturbation theory). The approa...