The maximal range problem for a quasidisk

✍ Scribed by Vladimir Andrievskii

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 202 KB
• Volume: 123
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1016/s0021-9045(03)00071-6

✦ Synopsis

Let GCC and DCC be simply connected domains such that 0AG-D: Denote by P n ; nAN :¼ f1; 2; yg; the set of all complex polynomials of degree at most n: Let P n ðG; DÞ :¼ fpAP n : pð0Þ ¼ 0; pðGÞCDg:

Our main purpose is to find how large, i.e., how close to D; the ''maximal polynomial range'' D n ðGÞ :¼ [ pAPnðG;DÞ pðGÞ can be. We consider G to be a quasidisk and D to be an arbitrary domain whose boundary consists of more than two points.

Published by Elsevier Science (USA).