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The Smirnov class f...
The Smirnov class for spaces with the complete Pick property
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- Aleman, Alexandru (author)
- Lund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Hartz, Michael (author)
- Washington University in St. Louis
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- McCarthy, John E. (author)
- Washington University in St. Louis
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- Richter, Stefan (author)
- University of Tennessee
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(creator_code:org_t)
- 2017-07-02
- 2017
- English.
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 96:1, s. 228-242
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Abstract
Subject headings
Close
- 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 Kaptanoğlu. 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Publication and Content Type
- art (subject category)
- ref (subject category)
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