Journal
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume 96, Issue -, Pages 228-242Publisher
WILEY
DOI: 10.1112/jlms.12060
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Funding
- Ontario Trillium Scholarship
- Feodor Lynen Fellowship
- National Science Foundation [DMS 1565243]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1565243] Funding Source: National Science Foundation
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We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptanoglu. We explore various consequences of this result regarding zero sets, spaces on compact sets and Gleason parts. In particular, using a construction of Salas, we exhibit a rotationally invariant complete Pick space of analytic functions on the unit disc for which the corona theorem fails.
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