Cantor sets and cyclicity in weighted Dirichlet spaces

Cantor sets and cyclicity in weighted Dirichlet spaces

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques.

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Veröffentlicht in:Journal of mathematical analysis and applications 2010, Vol.372 (2), p.565-573
Hauptverfasser: El-Fallah, O., Kellay, K., Ransford, T.
Format: Artikel
Sprache:eng
Schlagworte:
Cantor set
Classical Analysis and ODEs
Complex Variables
Cyclic vector
Dirichlet space
Exact sciences and technology
Mathematical analysis
Mathematics
Potential theory
Sciences and techniques of general use
Weight
α-capacity
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Beschreibung
Zusammenfassung:We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.07.047