Search results for " 42C15"

showing 5 items of 5 documents

Gabor systems and almost periodic functions

2017

Abstract Inspired by results of Kim and Ron, given a Gabor frame in L 2 ( R ) , we determine a non-countable generalized frame for the non-separable space AP 2 ( R ) of the Besicovic almost periodic functions. Gabor type frames for suitable separable subspaces of AP 2 ( R ) are constructed. We show furthermore that Bessel-type estimates hold for the AP norm with respect to a countable Gabor system using suitable almost periodic norms of sequences.

Almost periodic functionApplied Mathematics010102 general mathematicsAlmost-periodic functions010103 numerical & computational mathematicsGabor frame01 natural sciencesLinear subspaceFunctional Analysis (math.FA)Separable spaceCombinatoricsMathematics - Functional AnalysisFramesNorm (mathematics)42C40 42C15 42A75FOS: MathematicsAP-framesCountable set0101 mathematicsGabor systemsMathematicsAlmost-periodic functions; AP-frames; Frames; Gabor systems; Applied Mathematics
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Compactness of Fourier integral operators on weighted modulation spaces

2019

Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential operators.

Modulation spacePure mathematicsPseudodifferential operatorsApplied MathematicsGeneral Mathematics010102 general mathematicsMatrix representationGabor frame01 natural sciencesFourier integral operatorFunctional Analysis (math.FA)Mathematics - Functional Analysis35S30 47G30 42C15Compact spaceFOS: Mathematics0101 mathematicsMathematicsTransactions of the American Mathematical Society
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Weak A-frames and weak A-semi-frames

2021

After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a weak lower $A$-semi-frame and we study its properties. In particular, we compare it with that of lower atomic systems, introduced in (GB). We discuss duality properties and we suggest several possible definitions for weak $A$-upper semi-frames. Concrete examples are presented.

Numerical AnalysisPure mathematicsMatematikApplied MathematicsDensely defined operatorDuality (optimization)Functional Analysis (math.FA)41A99 42C15Mathematics - Functional AnalysisSettore MAT/05 - Analisi MatematicaA-frames weak (upper and lower) A-semi-frames lower atomic systems G-dualityFOS: MathematicsAnalysis$A$-framesweak (upper and lower) $A$-semi-frameslower atomic systems$G$-dualityMathematicsMathematics
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Distributions Frames and bases

2018

In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate, in particular, conditions for them to constitute a "continuous basis" for the smallest space $\mathcal D$ of a rigged Hilbert space. This analysis requires suitable extensions of familiar notions as those of frame, Riesz basis and orthonormal basis. A motivation for this study comes from the Gel'fand-Maurin theorem which states, under certain conditions, the existence of a family of generalized eigenvectors of an essentially self-adjoint operator on a domain $\mathcal D$ which acts like an orthonormal basis of the Hilbert space $\mathcal H$. The correspond…

Pure mathematicsGeneral Mathematics02 engineering and technologyBaseDistributionSpace (mathematics)01 natural sciencessymbols.namesakeSettore MAT/05 - Analisi MatematicaGeneralized eigenvector0202 electrical engineering electronic engineering information engineeringFOS: MathematicsFrameOrthonormal basisRigged Hilbert spaces0101 mathematicsMathematicsBasis (linear algebra)Applied MathematicsOperator (physics)010102 general mathematics47A70 42C15 42C30Hilbert space020206 networking & telecommunicationsRigged Hilbert spaceFunctional Analysis (math.FA)Mathematics - Functional AnalysisDistribution (mathematics)symbolsAnalysis
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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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