Topological and algebraic genericity of divergence and universality

Frédéric Bayart. "Topological and algebraic genericity of divergence and universality." Studia Mathematica 167.2 (2005): 161-181. <http://eudml.org/doc/284910>.

@article{FrédéricBayart2005,
abstract = {We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.},
author = {Frédéric Bayart},
journal = {Studia Mathematica},
keywords = {hypercyclicity; universal family; Dirichlet series; Fourier series; divergence; quasi-sure property; topological genericity; universal series},
language = {eng},
number = {2},
pages = {161-181},
title = {Topological and algebraic genericity of divergence and universality},
url = {http://eudml.org/doc/284910},
volume = {167},
year = {2005},
}

TY - JOUR
AU - Frédéric Bayart
TI - Topological and algebraic genericity of divergence and universality
JO - Studia Mathematica
PY - 2005
VL - 167
IS - 2
SP - 161
EP - 181
AB - We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.
LA - eng
KW - hypercyclicity; universal family; Dirichlet series; Fourier series; divergence; quasi-sure property; topological genericity; universal series
UR - http://eudml.org/doc/284910
ER -