Weak continuity and almost continuity

Almost Periodicity, Equi-continuity and Total Boundedness

Let X be a uniform space; that is to say, let X be a space provided with a system of indexed neighborhoods Ua(x) (x(EX, a=index), subject to the conditions (A. Weil) : (1) If xÇzX and if a is an index, then xÇzUa(x)\ (2) If a and /? are indices, then there exists an index y such that xÇzX implies U7(x)ÇZUa(x)r\Up(x); (3) If a is an index, then there exists an index /? such that x, y, zÇzX with ...

Weak continuity with structural constraints

Nonlinear regression and nonlinear regularization are two powerful approaches to segmentation and nonlinear filtering. In this correspondence, we propose a hybrid approach that effectively combines the best of both worlds and can be efficiently implemented via the Viterbi algorithm.

Automatic continuity of almost multiplicative maps between Frechet algebras

For Fr$acute{mathbf{text{e}}}$chet algebras $(A, (p_n))$ and $(B, (q_n))$, a linear map $T:Arightarrow B$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(Tab - Ta Tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{N}$, $a, b in A$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$...

Markovian Bridges: Weak continuity and pathwise constructions

A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a natural parameterization in terms of the state space of the process. In the context of Feller processes with continuous transition densities, we construct by weak convergence considerations the only ver...

Weak Forms of Continuity and Associated Properties