JournalsprimsVol. 41, No. 2pp. 259–279

Partial *-algebras of Distributions

  • Camillo Trapani

    Università degli Studi di Palermo, Italy
  • Francesco Tschinke

    Università degli Studi di Palermo, Italy
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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.

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Camillo Trapani, Francesco Tschinke, Partial *-algebras of Distributions. Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, pp. 259–279

DOI 10.2977/PRIMS/1145475353