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Multiplication operators with deficiency indices (p,p) and sampling formulas in reproducing kernel Hilbert spaces of entire vector valued functions
Copyright policy )Multiplication operators with deficiency indices (p,p) and sampling formulas in reproducing kernel Hilbert spaces of entire vector valued functions
Abstract A number of recent papers have established connections between reproducing kernel Hilbert spaces H of entire functions, de Branges spaces, sampling formulas and a class of symmetric operators with deficiency indices ( 1 , 1 ) . In this paper analogous connections between reproducing kernel Hilbert spaces of entire vector valued functions, de Branges spaces of entire vector valued functions, sampling formulas and symmetric operators with deficiency indices ( p , p ) are obtained. Enroute, an analog of L. de Branges' characterization of the reproducing kernel Hilbert spaces of entire functions that are now called de Branges spaces is obtained for the p × 1 vector valued case. A special class of these de Branges spaces of p × 1 vector valued entire functions is identified as a functional model for M. G. Krein's class of entire operators with deficiency indices ( p , p ) .
Microsoft Academic Graph classification: Discrete mathematics Class (set theory) Entire function Hilbert space Sampling (statistics) Characterization (mathematics) symbols.namesake Kernel (algebra) symbols Multiplication Vector-valued function Mathematics
Analysis
Analysis
Microsoft Academic Graph classification: Discrete mathematics Class (set theory) Entire function Hilbert space Sampling (statistics) Characterization (mathematics) symbols.namesake Kernel (algebra) symbols Multiplication Vector-valued function Mathematics
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!Abstract A number of recent papers have established connections between reproducing kernel Hilbert spaces H of entire functions, de Branges spaces, sampling formulas and a class of symmetric operators with deficiency indices ( 1 , 1 ) . In this paper analogous connections between reproducing kernel Hilbert spaces of entire vector valued functions, de Branges spaces of entire vector valued functions, sampling formulas and symmetric operators with deficiency indices ( p , p ) are obtained. Enroute, an analog of L. de Branges' characterization of the reproducing kernel Hilbert spaces of entire functions that are now called de Branges spaces is obtained for the p × 1 vector valued case. A special class of these de Branges spaces of p × 1 vector valued entire functions is identified as a functional model for M. G. Krein's class of entire operators with deficiency indices ( p , p ) .