The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of _C_∞-vectors of a self-adjoint operator, is considered in the framework of the so-called duality method. The multiplication is deﬁned by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain spaces, that are an abstract version of the Bessel potential spaces, are used to factorize the product.
Cite this article
Camillo Trapani, Francesco Tschinke, Partial *-algebras of Distributions. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 259–279DOI 10.2977/PRIMS/1145475353