Journal
ACTA APPLICANDAE MATHEMATICAE
Volume 150, Issue 1, Pages 81-101Publisher
SPRINGER
DOI: 10.1007/s10440-017-0095-4
Keywords
Reproducing pairs; Continuous frames; Upper and lower semi-frames
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Funding
- Austrian Science Fund (FWF) through the START-project FLAME (Frames and Linear Operators for Acoustical Modeling and Parameter Estimation) [Y 551-N13]
- Istituto Nazionale di Alta Matematica (GNAMPA project Proprieta spettrali di quasi *-algebre di operatori)
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We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several examples, both discrete and continuous, are presented.
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