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Multiplication operators with deficiency indices (p,p) and sampling formulas in reproducing kernel Hilbert spaces of entire vector valued functions

Authors: Harry Dym; Santanu Sarkar;

Multiplication operators with deficiency indices (p,p) and sampling formulas in reproducing kernel Hilbert spaces of entire vector valued functions

Abstract

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 ) .

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Subjects by Vocabulary

Microsoft Academic Graph classification: Discrete mathematics symbols.namesake Kernel (algebra) Class (set theory) Entire function Hilbert space symbols Sampling (statistics) Multiplication Characterization (mathematics) Vector-valued function Mathematics

Keywords

Analysis

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    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).
    8
    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).
    8
    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
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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).
BIP!Citations provided by BIP!
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.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Top 10%
Average
Average
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