Open AccessComposition operators and Schröder’s functional equation
Author(s) -
Joel H. Shapiro
Publication year - 1998
Publication title -
contemporary mathematics - american mathematical society
Language(s) - English
Resource type - Reports
SCImago Journal Rank - 0.106
H-Index - 12
eISSN - 1098-3627
pISSN - 0271-4132
DOI - 10.1090/conm/213/02861
Subject(s) - mathematics , composition (language) , pure mathematics , algebra over a field , linguistics , philosophy
In Schroder’s equation, φ is the given quantity, a holomorphic selfmap of the unit disc U = {z ∈ C : |z| < 1}, and the goal is to find λ ∈ C and f holomorphic on U so that (1) is satisfied. Schroder’s equation is, of course, the eigenvalue equation for the composition operator Cφ, defined by Cφf = f ◦φ, where, at least for now, f is allowed to range through the entire space H(U) of functions holomorphic on U . The study I want to describe begins with a question that has long intrigued me:
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom