Search results for "dual frames"

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Localization of the spectra of dual frames multipliers

2022

This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the paper is to give some results about the localization of the spectra of dual frames multipliers, i.e. to individuate regions of the complex plane containing the spectra using some information about the frames and the symbols.

Numerical AnalysisMatematikApplied MathematicsFunctional Analysis (math.FA)spectrumMathematics - Functional Analysisdual framesSettore MAT/05 - Analisi MatematicaFOS: Mathematicsmultipliers42C15 47A10 47A12multipliers;dual frames;spectrumAnalysisMathematics
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On some dual frames multipliers with at most countable spectra

2021

A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of some dual frames multipliers giving, in particular, conditions to be at most countable. The contribution extends the results available in literature about the spectra of Bessel multipliers with symbol decaying to zero and of multipliers of dual Riesz bases.

Pure mathematicsApplied MathematicsZero (complex analysis)Hilbert spaceFunctional Analysis (math.FA)Dual (category theory)Multiplier (Fourier analysis)Mathematics - Functional Analysissymbols.namesakeOperator (computer programming)Dual frames Invertibility Multipliers SpectraSettore MAT/05 - Analisi MatematicaFOS: MathematicssymbolsCountable set42C15 47A10 47A12MultiplicationBessel functionMathematics
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