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RESEARCH PRODUCT

Continuous frames for unbounded operators

Giorgia Bellomonte

subject

Unbounded operator42C15 47A05 47A63 41A65Pure mathematicsContinuous A-frames Continuous weak A-frames Continuous atomic systems Unbounded operatorsAlgebra and Number TheoryAtomic system010102 general mathematicsHilbert spaceOrder (ring theory)01 natural sciencesBounded operatorFunctional Analysis (math.FA)Mathematics - Functional AnalysisRange (mathematics)symbols.namesakeSettore MAT/05 - Analisi Matematica0103 physical sciencessymbolsFOS: Mathematics0101 mathematics010306 general physicsAnalysisMathematics

description

Few years ago G\u{a}vru\c{t}a gave the notions of $K$-frame and atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$ in order to decompose $\mathcal{R}(K)$, the range of $K$, with a frame-like expansion. These notions are here generalized to the case of a densely defined and possibly unbounded operator on a Hilbert space $A$ in a continuous setting, thus extending what have been done in a previous paper in a discrete framework.

yearjournalcountryeditionlanguage
2021-03-18
https://dx.doi.org/10.48550/arxiv.1912.13097