Open AccessComposition–differentiation operators on the Hardy space
Author(s) -
Mahsa Fatehi,
Christopher N. B. Hammond
Publication year - 2020
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14898
Subject(s) - algorithm , annotation , type (biology) , artificial intelligence , computer science , geology , paleontology
Let φ \varphi be a nonconstant analytic self-map of the open unit disk in C \mathbb {C} , with ‖ φ ‖ ∞ > 1 \|\varphi \|_{\infty }>1 . Consider the operator D φ D_{\varphi } , acting on the Hardy space H 2 H^{2} , given by differentiation followed by composition with φ \varphi . We obtain results relating to the adjoint, norm, and spectrum of such an operator.