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On the Minimum Modulus of Analytic Functions of Moderate Growth in the Unit Disc

On the Minimum Modulus of Analytic Functions of Moderate Growth in the Unit Disc We study the behavior of the minimum modulus of analytic functions in the unit disc in terms of $$\rho _\infty $$ ρ ∞ -order, which is the limit of the orders of $$L_p$$ L p -norms of $$\log |f(re^{i\theta })|$$ log | f ( r e i θ ) | over the circle as $$p\rightarrow \infty $$ p → ∞ . 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On the Minimum Modulus of Analytic Functions of Moderate Growth in the Unit Disc

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References (29)

Publisher
Springer Journals
Copyright
Copyright © 2015 by The Author(s)
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-015-0118-y
Publisher site
See Article on Publisher Site

Abstract

We study the behavior of the minimum modulus of analytic functions in the unit disc in terms of $$\rho _\infty $$ ρ ∞ -order, which is the limit of the orders of $$L_p$$ L p -norms of $$\log |f(re^{i\theta })|$$ log | f ( r e i θ ) | over the circle as $$p\rightarrow \infty $$ p → ∞ . 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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: May 15, 2015

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