# Remarks on the Bohr and Rogosinski phenomena for power series

Remarks on the Bohr and Rogosinski phenomena for power series The following problems are discussed in this work. 1. Asymptotics of the majorant function in the Reinhardt domains in \$\${\mathbb C^n}\$\$ . 2. The Bohr and Rogosinski radii for Hardy classes of functions holomorphic in the disk. 3. Neither Bohr nor Rogosinski radius exists for functions holomorphic in an annulus, with natural basis. 4. The Bohr and Rogosinski radii for the mappings of the Reinhardt domains into Reinhardt domains. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Remarks on the Bohr and Rogosinski phenomena for power series

, Volume 2 (1) – Jan 26, 2012
10 pages

/lp/springer-journals/remarks-on-the-bohr-and-rogosinski-phenomena-for-power-series-f0dw6YORdx
Publisher
Springer Journals
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-012-0024-7
Publisher site
See Article on Publisher Site

### Abstract

The following problems are discussed in this work. 1. Asymptotics of the majorant function in the Reinhardt domains in \$\${\mathbb C^n}\$\$ . 2. The Bohr and Rogosinski radii for Hardy classes of functions holomorphic in the disk. 3. Neither Bohr nor Rogosinski radius exists for functions holomorphic in an annulus, with natural basis. 4. The Bohr and Rogosinski radii for the mappings of the Reinhardt domains into Reinhardt domains.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Jan 26, 2012