Majorant Series

By Harold P. Boas. 2000

136 citations recorded by the source corpus.

. This article discusses questions in one and several complex variables about the size of the sum of the moduli of the terms of the series expansion of a bounded holomorphic function. Although the article is partly expository, it also includes some pre-viously unpublished results with complete proofs.

View Paper: https://www.semanticscholar.org/paper/ee558bf20e9d79f9c34de0b0f2521cbbd9eb182f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Bohr phenomenon for certain subclasses of harmonic mappings (2020, background): “We note that for certain functions f in F , the majorant series Mf (r) takes the values larger than 1 (see [14]).”
The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive (2009, methodology): “were established for n > 1. The paper of Boas and Khavinson aroused new interest in the Bohr radius and has been a source of inspiration for many subsequent papers. For some time (see for instance [4]) it was thought that the left-hand side of (9) could not be improved. However, using (7), A. Def”
Bohr radius for certain classes of starlike and convex univalent functions (2020, background): “The Bohr’s inequality has been extended to several complex variables by finding the multidimensional Bohr radius (see [5, 6, 7, 14, 15]).”
Bohr's inequality for uniform algebras (2004, background): “See Aizenberg [1], Boas and Khavinson [2], Boas [3], for further connections and references.”