On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functionals and operator kernels as elements of dual spaces. A large class of examples is provided by pseudodifferential operators acting on Colombeau algebras. By a refinement of symbol calculus we review a new characterization of the wave front set for generalized functions with applications to microlocal analysis

Total boundedness in probabilistic normed spaces

In this paper, we study total boundedness in probabilistic normed space and we give criterion for total boundedness and D-boundedness in these spaces. Also we show that in general a totally bounded set is not D-bounded