Composition operators in the Dirichlet series setting

Hervé Queffélec. "Composition operators in the Dirichlet series setting." Banach Center Publications 75.1 (2007): 261-287. <http://eudml.org/doc/281887>.

@article{HervéQueffélec2007,
abstract = {In this work, we begin with a survey of composition operators on the Hardy space H² and on the Wiener algebra A⁺ of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D.~Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H² and A⁺ in the setting of Dirichlet series. We are led to the intermediate study of Taylor series in several, or countably many, variables. We finish with some open problems.},
author = {Hervé Queffélec},
journal = {Banach Center Publications},
keywords = {composition operators; boundedness; compactness; Hardy space; Dirichlet series; Wiener algebra},
language = {eng},
number = {1},
pages = {261-287},
title = {Composition operators in the Dirichlet series setting},
url = {http://eudml.org/doc/281887},
volume = {75},
year = {2007},
}

TY - JOUR
AU - Hervé Queffélec
TI - Composition operators in the Dirichlet series setting
JO - Banach Center Publications
PY - 2007
VL - 75
IS - 1
SP - 261
EP - 287
AB - In this work, we begin with a survey of composition operators on the Hardy space H² and on the Wiener algebra A⁺ of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D.~Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H² and A⁺ in the setting of Dirichlet series. We are led to the intermediate study of Taylor series in several, or countably many, variables. We finish with some open problems.
LA - eng
KW - composition operators; boundedness; compactness; Hardy space; Dirichlet series; Wiener algebra
UR - http://eudml.org/doc/281887
ER -