  In a recent paper, we gave a topological description of Colombeau type
algebras introducing algebras of sequences with exponential weights. Embeddings
of Schwartz' spaces into the Colombeau algebra G are well known, but for
ultradistribution and periodic hyperfunction type spaces we give new
constructions. We show that the multiplication of regular enough functions
(smooth, ultradifferentiable or quasianalytic), embedded into corresponding
algebras, is the ordinary multiplication.
