Annular functions in probability
| Autor: | Russell W. Howell |
|---|---|
| Rok vydání: | 1975 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 52:217-221 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1975-0374398-2 |
| Popis: | A function f f holomorphic in the open unit disk U U is said to be strongly annular if there exists a sequence { C n } \{ {C_n}\} of concentric circles converging outward to the boundary of U U such that the minimum of | f | |f| on C n {C_n} tends to infinity as n n increases. We show here that such functions with Maclaurin coefficients ± 1 \pm 1 form a residual set in the space of functions with coefficients ± 1 \pm 1 . We also show that the set of t t in [ 0 , 1 ] [0,1] for which ∑ r n ( t ) z n \sum {{r_n}(t){z^n}} is strongly annular ( r n {r_n} is the n n th Rademacher function) is residual, and measurable with measure either 0 0 or 1 1 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|