2017 •
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
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 (...)
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 ) . (Read More)
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