Abstract
Let f be a function meromorphic on the open unit disk D , with angular boundary limits bounded by one in modulus almost everywhere on the unit circle. We give sufficient conditions in terms of boundary asymptotics at finitely many points on the unit circle T for f to be a ratio of two finite Blaschke products. A necessary condition is that f has finitely many poles in D , i.e., that f is a generalized Schur function. Similar rigidity statements are presented for generalized Caratheodory and generalized Nevanlinna functions. Mathematics subject classification (2000): 30E05.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
