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Orbits of operators commuting with the Volterra operator
- Source :
- Journal de Mathématiques Pures et Appliquées. 89(2):145-173
- Publication Year :
- 2008
- Publisher :
- Elsevier BV, 2008.
-
Abstract
- Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L p [ 0 , 1 ] , with 1 ⩽ p ⩽ ∞ , are obtained. The results apply not only to the Riemann–Liouville operator V r and to I + V r with r > 0 , but also to operators of the form ϕ ( V ) , where ϕ is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann–Liouville operator as well as the Volterra operator can be related to the Levin–Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy–Carleman theorem, are needed to analyze the behavior of the orbits of I − c V , where c > 0 . The results are applied to the study of cyclic properties of ϕ ( V ) , where ϕ is a holomorphic function at 0.
- Subjects :
- Integral operators
Pure mathematics
Mathematics(all)
Volterra operator
Mathematics::Complex Variables
General Mathematics
Applied Mathematics
Mathematical analysis
Holomorphic functional calculus
Holomorphic function
Zero (complex analysis)
Orbits
Volterra operators
Supercyclic operator
Operator (computer programming)
Commuting operators
Cyclic operator
Mathematics
Subjects
Details
- ISSN :
- 00217824
- Volume :
- 89
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Journal de Mathématiques Pures et Appliquées
- Accession number :
- edsair.doi.dedup.....d95d2bdb63068be4b064f5f24443a5ed
- Full Text :
- https://doi.org/10.1016/j.matpur.2007.10.002