ABSTRACT
When solving the problem of the multiplication of generalized functions, physicists and mathematicians regard a generalized function as an equivalence class of sequences of C∞-functions. A general method of constructing such algebras was obtained by A. B. Antonevich and Ya. V. Radyno. This chapter reintroduces the topology on the space in a different way. It has been found that this method can be applied not only to generalized functions but also to objects of different character, for example, to unbounded operators. The chapter describes that the proposed ideas and approaches will permit one to solve nonlinear problems and in particular, certain problems of Quantum field theory.
