Open Access
Spring 2017 Reproducing pairs of measurable functions and partial inner product spaces
Jean-Pierre Antoine, Camillo Trapani
Adv. Oper. Theory 2(2): 126-146 (Spring 2017). DOI: 10.22034/aot.1611-1053


We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.


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Jean-Pierre Antoine. Camillo Trapani. "Reproducing pairs of measurable functions and partial inner product spaces." Adv. Oper. Theory 2 (2) 126 - 146, Spring 2017.


Received: 7 November 2016; Accepted: 22 February 2017; Published: Spring 2017
First available in Project Euclid: 4 December 2017

zbMATH: 1368.42029
MathSciNet: MR3730064
Digital Object Identifier: 10.22034/aot.1611-1053

Primary: 41A99
Secondary: 46Bxx , 46C50 , 46Exx

Keywords: continuous frames , lattices of Banach spaces , partial inner product spaces , reproducing pairs , upper and lower semi-frames

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.2 • No. 2 • Spring 2017
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