Treffer: Remarks on the Bohr Phenomenon: Remarks on the Bohr phenomenon
Title:
Remarks on the Bohr Phenomenon: Remarks on the Bohr phenomenon
Authors:
Source:
Computational Methods and Function Theory. 4:1-19
Publisher Information:
Springer Science and Business Media LLC, 2004.
Publication Year:
2004
Subject Terms:
\(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables, Hardy spaces, Banach spaces of continuous, differentiable or analytic functions, Taylor series, Spaces of bounded analytic functions of one complex variable, 0101 mathematics, Bohr's theorem, Schwarz-Pick estimates, 01 natural sciences, Power series, series of functions of several complex variables, Bohr radius
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
2195-3724
1617-9447
1617-9447
DOI:
10.1007/bf03321051
Access URL:
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....e7a88c07e1047aeabd724e9ca9258b80
Database:
OpenAIRE
Weitere Informationen
In 1914 Harald Bohr published the following surprising result: If \(f(z)=\sum a_n z^n\) is an analytic functions on the unit disc such that \(| f(z)| \leq 1\) for each \(z\) in the disc, then \(\sum | a_n z^n | \leq 1\) when \(| z| \leq 1/3\), and moreover the radius \(1/3\) is best possible. The authors note that no such Bohr phenomenon occurs if the space \(H^{\infty}\) is replaced by a Hardy space \(H^q, 0 < q < \infty\). In fact, there is no \(00\), particularly when \(0