Search results for " 46A13"

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Rigged Hilbert spaces and contractive families of Hilbert spaces

2013

The existence of a rigged Hilbert space whose extreme spaces are, respectively, the projective and the inductive limit of a directed contractive family of Hilbert spaces is investigated. It is proved that, when it exists, this rigged Hilbert space is the same as the canonical rigged Hilbert space associated to a family of closable operators in the central Hilbert space.

Pure mathematicsMathematics::Operator AlgebrasGeneral MathematicsHilbert spaceRigged Hilbert spaceDirect limitPhysics::Classical PhysicsFunctional Analysis (math.FA)Mathematics - Functional Analysissymbols.namesakeSettore MAT/05 - Analisi Matematica47A70 46A13 46M40Mathematics::Quantum AlgebrasymbolsFOS: MathematicsRigged Hilbert spaces · Inductive and projective limitsMathematics
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Frames and representing systems in Fréchet spaces and their duals

2014

[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.

Pure mathematicsRelation (database)(LB)-spacesrepresenting systems010103 numerical & computational mathematics01 natural sciencesMathematical research46A04 42C15 46A13 46E10Fréchet spacesweakly sufficient setssymbols.namesake$(LB)$-spacesDIDACTICA DE LA MATEMATICA0101 mathematics46A1346E10Dirichlet seriesMathematicsAlgebra and Number Theory42C15Group (mathematics)010102 general mathematicsSampling (statistics)Representing systemsMathematics - Functional AnalysisFramesframessymbolsDual polyhedronWeakly sufficient setsFrechet spacesMATEMATICA APLICADAAnalysisBessel function46A04Analytic function
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