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On maximal ranges of polynomial spaces in the unit disk

✍ Scribed by Antonio Y. Cordova; Stephan Ruscheweyh

Publisher: Springer
Year: 1989
Tongue: English
Weight: 731 KB
Volume: 5
Category: Article
ISSN: 0176-4276
DOI: 10.1007/bf01889612

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## Abstract Let ‖ · ‖ denote the uniform norm in the unit disk of the complex plane ℂ. The main result in this note is as follows: __For any complex polynomial P of degree at most n and any α__ ∈ ℂ __the inequality__ ‖__P__ ‖ ⩽ (__n__ + 1)(‖__z P__ (__z__) + __α__ ‖ ‐ |__α__ |) __holds.__ For any