Algebras of distributions suitable for phase-space quantum mechanics. III. The dual space of the algebra L_b(S)

The strong dual space of the topological algebra L_b(S), where S is the Schwartz space of smooth declining functions on R, may be obtained as an inductive limit of projective limits of Hilbert spaces. To that end, we construct a symbol calculus for elements of L_b(S,S'). We show that the dual space is a dense ideal in L_b(S) itself, and can be given the structure of a Q-algebra with continuous quasiinversion.Universidad de Costa Rica/[]/UCR/Costa RicaUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic