On the Minimum Modulus of Analytic Functions of Moderate Growth in the Unit Disc
| Autor: | Igor Chyzhykov, M. Kravets |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Modulo operation
Applied Mathematics 010102 general mathematics Mathematical analysis Order (ring theory) Modulus 01 natural sciences 010101 applied mathematics Combinatorics Computational Theory and Mathematics Harmonic function Factorization Limit (mathematics) 0101 mathematics Unit (ring theory) Analysis Analytic function Mathematics |
| Zdroj: | Computational Methods and Function Theory. 16:53-64 |
| ISSN: | 2195-3724 1617-9447 |
| Popis: | We study the behavior of the minimum modulus of analytic functions in the unit disc in terms of \(\rho _\infty \)-order, which is the limit of the orders of \(L_p\)-norms of \(\log |f(re^{i\theta })|\) over the circle as \(p\rightarrow \infty \). This concept coincides with the usual order of the maximum modulus function if the order is greater than one. New results are obtained for analytic functions of order smaller than 1. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink