Extensions of Bernstein's theorem on absolutely monotonic functions

✍ Scribed by G.G. Bilodeau

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 233 KB
• Volume: 116
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1016/s0022-247x(86)80013-0

✦ Synopsis

The main result is that D~[ea°~f(x)] >10 for n~>0 on [a, b] implies that f is analytic on [a, b) if lira a,,/n < ~ where {a,} is a non-decreasing sequence of nonnegative numbers. The result is best possible in a well defined sense.