Compositional frequent hypercyclicity on weighted Dirichlet spaces
Bernal-Gonzàlez, Luis ; Bonilla, Antonio
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 1-11 / Harvested from Project Euclid
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It is proved that, in most cases, a scalar multiple of a linear-fractional generated composition operator $\lambda C_\varphi$ acting on a weighted Dirichlet space $S_\nu$ of holomorphic functions in the open unit disk is frequently hypercyclic if and only if it is hypercyclic. In fact, this holds for all triples $(\nu ,\lambda , \varphi )$ with the possible exception of those satisfying $\nu \in [1/4,1/2), \, |\lambda | = 1, \, \varphi =$ a parabolic automorphism.
Publié le : 2010-02-15
Classification:  composition operator,  chaotic operator,  frequently hypercyclic operator,  weighted Dirichlet spaces,  47A16,  30E10,  30H05,  47B33,  47B38 
@article{1267798495,
     author = {Bernal-Gonz\`alez, Luis and Bonilla, Antonio},
     title = {Compositional frequent hypercyclicity on weighted Dirichlet spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 1-11},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1267798495}
}

Bernal-Gonzàlez, Luis; Bonilla, Antonio. Compositional frequent hypercyclicity on weighted Dirichlet spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  1-11. http://gdmltest.u-ga.fr/item/1267798495/