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Compact composition operators with non-linear symbols on the H2 space of Dirichlet series

Bayart, Frederic; Brevig, Ole Fredrik
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2492761
Date
2017
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  • Institutt for matematiske fag [2673]
  • Publikasjoner fra CRIStin - NTNU [41874]
Original version
Pacific Journal of Mathematics. 2017, 291 (1), 81-120.   10.2140/pjm.2017.291.81
Abstract
We investigate compactness of composition operators on the Hardy space of Dirichlet series induced by a map φ(s)=c0s+φ0(s), where φ0 is a Dirichlet polynomial. Our results depend heavily on the characteristic c0 of φ and, whenc0=0, on both the degree of φ0 and its local behavior near a boundary point. We also study the approximation numbers for some of these operators. Our methods involve geometric estimates of Carleson measures and tools from differential geometry.
Publisher
Mathematical Sciences Publishers (MSP)
Journal
Pacific Journal of Mathematics

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