Regular functions transversal at infinity

INCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

Fractality and Lapidus zeta functions at infinity

We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and demonstrate its use in analysis of fractal properties of unbounded sets at infinity. AMS subject classifications: 11M41, 28A12, 28A75, 28A80, 28B15, 42B20, 44A05, ...

inclusion relations concerning weakly almost periodic functions and functions vanishing at infinity

we consider the space of weakly almost periodic functions on a transformation semigroup (s, x , ?) and show that if x is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of s on x, then every continuous function on x, vanishing at infinity is weakly almost periodic. we also use a number of diverse examples to show that th...

New results on the order of functions at infinity

Decay at Infinity of Caloric Functions within Characteristic Hyperplanes

It is shown that a function u satisfying, |∆u+∂tu| ≤ M (|u|+ |∇u|), |u(x, t)| ≤ MeM|x| 2 in R × [0, T ] and |u(x, 0)| ≤ Cke −k|x| in R and for all k ≥ 1, must vanish identically in R × [0, T ].