6533b824fe1ef96bd127ffc5
RESEARCH PRODUCT
Partial Multiplication of Operators in Rigged Hilbert Spaces
Francesco TschinkeCamillo Trapanisubject
Pure mathematicsAlgebra and Number TheoryNuclear operatorHilbert spaceRigged Hilbert spaceOperator theorySpace (mathematics)Compact operator on Hilbert spaceAlgebrasymbols.namesakeSchwartz spacesymbolsAnalysisSelf-adjoint operatorMathematicsdescription
The problem of the multiplication of operators acting in rigged Hilbert spaces is considered. This is done, as usual, by constructing certain intermediate spaces through which the product can be factorized. In the special case where the starting space is the set of C∞-vectors of a self-adjoint operator A, a general procedure for constructing a special family of interspaces is given. Their definition closely reminds that of the Bessel potential spaces, to which they reduce when the starting space is the Schwartz space \(\mathcal{S}(\mathbb{R}^n ).\) Some applications are considered.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-04-01 | Integral Equations and Operator Theory |