preprint
Algebras of distributions suitable for phase-space quantum mechanics. III. The dual space of the algebra L_b(S)
Autor
Gracia Bondía, José M.
Várilly Boyle, Joseph C.
Figueroa González, Héctor
Institución
Resumen
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.