hilbert function spaces
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scholarly journals Interpolating Sequences in Spaces with the Complete Pick Property

2017 ◽  
Vol 2019 (12) ◽  
pp. 3832-3854 ◽  
Author(s):  
Alexandru Aleman ◽  
Michael Hartz ◽  
John E McCarthy ◽  
Stefan Richter
Keyword(s):  
Hardy Space ◽  
Carleson Measure ◽  
Hilbert Function ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Interpolating Sequences ◽  
Hilbert Function Spaces ◽  
Multiplier Algebras

Abstract We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.

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