Hermitian composition operators on Hardy-Smirnov spaces

@article{GajathGunatillake2017,
abstract = {Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f ⃘ φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.},
author = {Gajath Gunatillake},
journal = {Concrete Operators},
keywords = {Composition operator; Hermitian operator; Hardy-Smirnov space; composition operator},
language = {eng},
number = {1},
pages = {7-17},
title = {Hermitian composition operators on Hardy-Smirnov spaces},
url = {http://eudml.org/doc/288053},
volume = {4},
year = {2017},
}

TY - JOUR
AU - Gajath Gunatillake
TI - Hermitian composition operators on Hardy-Smirnov spaces
JO - Concrete Operators
PY - 2017
VL - 4
IS - 1
SP - 7
EP - 17
AB - Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f ⃘ φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.
LA - eng
KW - Composition operator; Hermitian operator; Hardy-Smirnov space; composition operator
UR - http://eudml.org/doc/288053
ER -