dc.contributor.author
Nicolau, A.
dc.date.accessioned
2023-09-14T13:51:20Z
dc.date.accessioned
2024-09-19T14:35:12Z
dc.date.available
2023-09-14T13:51:20Z
dc.date.available
2024-09-19T14:35:12Z
dc.date.issued
2022-05-01
dc.identifier.uri
http://hdl.handle.net/2072/536903
dc.description.abstract
Let f be an inner function with f(0)=0 which is not a rotation and let fn be its n-th iterate. Let {an} be a sequence of complex numbers. We prove that the series ∑anfn(ξ) converges at almost every point ξ of the unit circle if and only if ∑|an|2<∞. The main step in the proof is to show that under this assumption, the function F=∑anfn has bounded mean oscillation. We also prove that F is bounded on the unit disc if and only if ∑|an|<∞. Finally we describe the sequences of coefficients {an} such that F belongs to other classical function spaces, as the disc algebra and the Dirichlet class. © 2022 Elsevier Masson SAS
eng
dc.description.sponsorship
Generalitat de Catalunya: 2017 SGR 395; Ministerio de Economía y Competitividad, MINECO: MTM2017-85666-P
dc.format.extent
28 p.
cat
dc.publisher
Elsevier Masson s.r.l.
cat
dc.relation.ispartof
Journal de Mathematiques Pures et Appliquees
cat
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Bounded mean oscillation; Dirichlet class; Hardy spaces; Inner function
cat
dc.title
Convergence of linear combinations of iterates of an inner function
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/submittedVersion
cat
dc.identifier.doi
10.1016/j.matpur.2022.03.003
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
