Search results for "41A99"

showing 3 items of 3 documents

Reproducing pairs of measurable functions and partial inner product spaces

2016

We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.

Mathematics - Functional Analysi41A99 46Bxx 46C50 46Exx
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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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Reproducing pairs of measurable functions

2017

We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several examples, both discrete and continuous, are presented.

continuous framesPure mathematicsPartial differential equationMeasurable functionApplied Mathematics010102 general mathematicsBanach spaceupper and lower semi-frames01 natural sciencesDual (category theory)Functional Analysis (math.FA)010101 applied mathematicsMathematics - Functional AnalysisContinuous frameReproducing pairInner product spaceSettore MAT/05 - Analisi MatematicaReproducing pairsUpper and lower semi-frameFOS: Mathematics0101 mathematics41A99 46Bxx 46ExxMathematics
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