Search results for "Fréchet spaces"

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Shrinking and boundedly complete Schauder frames in Fréchet spaces

2014

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsShrinkingReflexivitySchauder basisFunction space(LB)-spacesApplied MathematicsMathematics::Analysis of PDEsConvex setMathematics::General TopologyFréchet spacesSchauder basisAtomic decompositionSchauder fixed point theoremSchauder frameLocally convex spacesLocally convex topological vector spaceBoundedly completeDual polyhedronAtomic decompositionMATEMATICA APLICADAAnalysisMathematics
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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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